There is no absolute set answer. The necessary joist height (thickness) depends in part on the distances you are trying to span. It also depends on the load you will be putting on the joist, how widely you space your joists, and the type of wood your joists are made of. A good grade of 2X10 lumber might be used for joists spaced 16 inches apart where the longest clear span is no more than say 15 feet. If you needed to span a room that is 20 feet across with lumber of the same quality, you might need to use 2x12s that were spaced no wider than every 12 inches. You mentioned a 7000 square foot home. I would lay odds that you intend to have large open rooms downstairs. That fact alone means you will need thicker joists. The whole issue of space between the floors for can lights and ductwork is secondary compared to making sure that your joists will support the load that is put on them. This is NOT an area that a novice should be playing around in. I have an undergraduate minor in physics and despite having recently read far more about joist loads and span table that I ever wanted to, and I can barely comprehend the subject. I would NEVER trust myself to actually try to determine the proper size joists for a house without help from a structural engineer. And frankly, I rather doubt most architects - who are only required to take a very minimal amount of physics to get their degrees - really understand span load tables either. I suspect (pray) they confer with qualified structural engineers whenever they are designing anything out of the ordinary. But, let me give you two examples and tell a cautionary tale... In our current house, the joists are 2x12 lumber. (I know b/c several years ago I repaired the sheetrock in the dining room after we had a leaking pipe.) However, our current house is a very simple rectangular shape of only 1900 sq feet. It has a central staircase with rooms on either side. The joists between the 1st and 2nd floor run perpendicular to the staircase and the widest room they have to span is only 14.5 ft wide. The HVAC unit also sits in the middle of the house (behind and just to one side of the staircase) so the AC ducts run parallel to the joists (i.e., each duct lies between two joists) to reach the rooms on either side of the staircase. A soffit over my kitchen cabinets houses a duct that runs perpendicular to the joists from the HVAC unit to the back of the house. Parallel ducts T out of the top of this to reach the rooms that are at the back of the house. No holes had to be cut thru the joists to accomodate the ductwork. Meanwhile, all our upstairs plumbing is centralized over a single "wet wall" so all the drainage pipes run straight down. Again, no need to cut holes thru those 12 inch joists. The only holes drilled through our 12 inch joists are little tiny ones that accomodate electrical wiring. Now the second example and the cautionary tale... Our new home - still under construction - is a 3200 sq ft house with a much more complex design with much larger rooms downstairs. I will also have two large cast-iron bathtubs upstairs and wanted to be sure their weight, when filled, would not be a problem. My architect and his engineer specified 18" deep open-web trusses spaced 16 inches on center. To save money however, my builder elected to use 18 inch i-beams joists made of oriented strand board (OSB) instead. (Actually OSB is stronger than real lumber when used for ibeams.) The engineer at the lumber store where my builder bought his lumber package told the builder he could place safely place the OSB ibeam joists 24 inches apart. I was out of town for several days while framing was going on so first time I saw the i-beam trusses, my builder was already framing up the second floor. I immediatley insisted that he stop what he was doing and verify with his engineers that he would be able to cut large enough holes thru the ibeams to accomodate my HVAC ducts BEFORE he went any further. I should have just told my builder he had to follow the specs but I was trying to be reasonable. I told him that IF holes could be cut through those ibeam joists large enough to accomodate HVAC ducts without compromising their structural integrity, he could go ahead and use them. But, if not, he needed to back up, take down the second floor framing, and replace the ibeams with the open web trusses specified in the plans. Two days later, in one of many many lies he told me, my builder said he had checked with his engineer and that the HVAC ducts would be "no problem"... that I should "trust him" and "let him do his job" because he was a professional. Foolishly, I did so. Later - after my house was fully framed, sheathed, roofed, shingled, sided with Hardie, had all windows and doors installed, and the exterior was painted - I learned for the first time what my builder meant by "no problem." It meant he had unilaterally decided that he would move the two HVAC units and ductwork up into the attic so holes would not have to be cut thru the ibeams for the ductwork! He completely ignored the fact that this decision meant the HVAC would no longer be in the heated and cooled envelope of the house which would increase my utility bills AND require him to purchase larger and more costly HVAC units; that running flex duct down from the attic to the first floor rooms required chases which took significant amounts of space out of each of my bedroom closets; and that positioning two HVAC units and a spiderweb of flex duct in the attic made it completely impossible to ever consider putting in an attic bedroom - which was the whole reason I had elected to have a 12/12 stick built roof in the first place! But my cautionary tale continues... It then turned out that the necessary holes for the plumbing drainage pipes was too much for the joists! In some cases the joists span distances of 25 feet. Once the plumber cut a 4 inch diameter hole through several joists to accomodate a toilet drainage pipe, the joists started bowing inward. I noticed rather quickly that the sub-floors on the second floor were no longer level. My builder tried to tell me that it was "normal" for the subfloors to bow a little but that putting the final layer of flooring on top would correct the problem! HAH! By this point, I was long past trusting anything the man said. We are building out in the country where no inspections are required except for septic systems but I had included in my contract a provision allowed me to call in an independant third-party inspector at any point. The contract stated that the third-party inspector's finding and recommendations regarding the safety or structural integrity of any element in the house would be controling. In other words, if the inspector said something needed to be done, builder had to do it at his cost. The inspector required my builder to go back and put an additional 18 inch i-beam joist between every pair of existing joists that had had a hole cut thru it. So now the joists are spaced every 12 inches instead of every 24 inches and the second floor no longer bows. I don't know what it cost my builder to put in the additional joists and then to replace the drain pipe he had to cut... but I'd lay odds the total cost was more than if he'd used the open web trusses in the first place. In case you're wondering, we ultimately fired the builder and filed suit against him after even more issues reflecting his incompetance and dishonesty. Now I'm the GC to finish the build... and believe me, I'm relying heavily on my third-party inspector to help me get things done right! The bottom line, simply by asking "10 inches or 18 inches? which one is the correct answer?" you reveal that you have a lot to learn before you proceed. You might start by reading this link. Here is a link that might be useful: Tutorial on joist design

This has been very interesting as I have the same predicament. It's not really encouraging me to rush into doing this. Fortunately I don't do much of any greasy cooking and I have a nearby external exhaust fan in my laundry room to suck out odors. The biggest concern is moisture wafting up on the cabinets but aside from sticky grime that I cleaned off from previous owners, the cabinets are in fine condition even after 15 years without external exhaust. What I have been pondering is if I could somehow connect into that laundry duct work through the attic as I don't really need an exhaust fan in the laundry room.

The apparent contradiction of cooling inadequacy vs. heating sufficiency is not a contradiction at all. It is basic physics and it can not be messed with. If you have the heat transfer rates and capacities/contributions of both heating and cooling appliances arithmetic will make sense of it. I specify contribution because you need to know if they are operating up to their rated capacity. Condition of the ducts also contributes, to both heating and cooling as you pointed out. Of course, and the calculations involving existing construction vs. new construction is sometimes challenging due to unknowns in the old stuff. Rather than estimates of heat transfer using assumptions about the construction, you can do better with fuel use rates. You should be able to get real heat contribution from the furnace and fuel use records (and heating degree days) from the coldest weeks of the year when space heating makes hot water and cooking insignificant. You also need to know the efficiency of the furnace. An energy rater or engineer should be able to use that data to calculate the heat transfer rates of the structure. (BTU in must equal BTU out.) Those rates can also be used for heat transfer in the other direction in the summer. Those calculations can be done today. You have fuel use records and you can get degree days from a nearby weather station. It is somewhat less common to use energy use of the cooling appliance for estimates, but it should work just as well. You need to separate electricity use by installing a separate meter and the contribution of humidity removal will have to be factored in. That means that you'd have to record humidity inside and outside and include that in the calculation. It is likely that you have sufficient capacity for you furnace or it is oversized whereas the cooling capacity is not adequate if your cooling unit is functioning properly. Again, calculations will tell you. How do you fix it? Better insulation on the ducts, structure envelope and better sealing of both will always cost less in the long run than installing a larger appliance. Bringing the ducts indoors is also a good idea as pointed out by mike_home. Don't think of active fans if you consider better attic ventilation. It needs to be passive. it is difficult, however, to draw enough air through an attic to make much of a difference in its temperature. Most of the heat transfer into the living space is due to re-radiation of heat from the underside of the roof deck. That is why radiation barriers were so "hot" for a time. The trouble with them is that they get dirty and lose effectiveness pretty quickly. It was a nice idea, but did not work as expected.

If the house is designed to current IECC energy codes or better, the 1st level radiant could probably handle most of the home's heating loads including 2nd level. If upfront costs and operating costs are important, you may want to reconsider radiant floors and propane as main energy source. Here is [recent thread on propane[(https://www.houzz.com/discussions/energy-star-most-efficient-2019-boilers-help-reading-the-stats-dsvw-vd~5649781?n=36) boilers. To summarize, propane is the most expensive common fuel. It would cost less to heat your home using electricity, as long as you choose high efficiency heat pump options. Cold climate heat pumps are available for your climate so choose a contractor who is comfortable with them and follow their guidance on any needed backup. Tough to beat woodstove with frequent power outages. Radiant only provides heating so it's a tougher choice if the upgrade costs are worthwhile in your climate. Cold climate heat pumps can satisfy heating needs with generally less upfront costs. Ductless heat pumps are packaged systems that are easy to install. Providing sweat equity for radiant floors will be needed to compete in upfront costs. Tubing, manifolds, pumps, appliances, controls, pipes, all done in custom snowflake fashion. Giant propane tank, piped fos$il fuels into house, combustion exhaust to expel, hopefully not backdraft. Most people choosing radiant are going off experience based on inefficient homes. Building to current codes changes the comfort dynamic and some find radiant less comfortable due to thermostat delay response. Radiant floors rarely make economic sense for efficient homes.