You don't say where you live, but if you live some place with extreme temperatures in the summer or winter, in addition to ridding your home of asbestos, you'll probably get much more efficient heating and cooling if you replace your existing duct work with modern, insulated and properly-sized ducting. And, since old ducting is notorious for leaking, you can solve that problem, too. New ducting also makes it an easy matter to add, move or enlarge registers, which can improve heating and cooling. Only licensed and certified contractors are allowed to remove asbestos, and you'll need special permits for both the removal and disposal, but the contractor should take care of that for you. Once the work begins, it goes very quickly, and is usually done within a day, including any clean-up. These guys are specialists, and know how to get the job done safely and efficiently. You won't miss your old ducting, but you'll be much happier with modern insulated duct work that doesn't leak. Properly-sized and insulated ducting will likely reduce noise from your HVAC system, too.

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.

"The manufacturers of Vent Hoods are miseducating the consumers." Yes. Somewhat. Not really. They are in business to make money and they do that by making hoods as inexpensively as possible and then selling as many as they can for as much money as they can. Their goal is NOT your health or the IAQ of your home - that is up to you. Telling consumers that they'll also need to spend money on MUA if they buy hood X will negatively impact their sales (ignorant consumer will just go buy a hood from brand Y instead because it doesn't say you need MUA even though it has an identical need for MUA) so they do not want to do that. MUA is also not something that fits well within consumer hood manufacturers world except to the extent that they might offer a hood w/ integrated front curtain ducting. It is much more of a pure HVAC thing. It can be supplied to the return ducts of an HVAC system, the supply ducts or ducted directly to appropriate locations. Incoming air can be heated by gas, electric or hydronic. Incoming air may need to be humidified or dehumidified. It often needs to be electrically integrated with the HVAC system controllers to function properly. Consumer hood manufacturers - ARE NOT IAQ or HVAC people or engineers - they make something decorative that by nature must include air movement so they reluctantly include air movement in their product. Commercial hood manufacturers - ARE IAQ and HVAC people and engineers. Their customers are much more educated than consumers. The one singular purpose of the product they are selling is IAQ - so they design and sell systems that provide good IAQ. Aesthetics is quite secondary for them. Residential HVAC companies in the U.S. - ARE NOT IAQ people (they should be though). A tiny few, less than about 1%, know it well and a few more know it a very little but the vast majority know just enough, based on what they've been told at a 4 hr CEU course, to sound like they know what they're talking about but they don't really understand it. Most residential HVAC people do not understand air movement or why things are done the way they are - they only know how to use tables that tell them to do this or that and as soon as something is outside of defined parameters they're totally lost (though sometimes don't even realize that they're lost). Licensed Professional Engineers do (or most do, some don't) understand air movement and other elements. They are the people who create the tables that HVAC people use. They can think independently. Defined parameters for them are not tables but the physics of air - it's movement, temperature and components. Unfortunately, most U.S. engineers do not have a good understanding of human physiology (except perhaps for biomedical engineers). They do not, for instance, understand how CO2 functions in our bodies and how high levels of CO2 due to poor ventilation affect us. Or how poor ventilation resulting in high levels of VOC's, PM, Carcinogens and Pathogens affect us.

OK - No duct cleaning for now. Still have issues. We moved in on May 9, 2022. New A/C was installed in March 2022. Home inspector said all ductwork was connected. Only issue was one run had some loose insulation. A manager from the company that installed the A/C spent 2 hours testing/adjusting the unit. He said it had full charge of freon. He tried changing fan speed and balancing. He could never get any improvement of the 11 degrees differential between return air and output air (unit ran for nearly an hour). No matter how much the unit runs, the humidity never falls below 70% (outdoor humidity between 40-50%). Does anybody have any suggestions as to what else might be check/tested?