This has the potential to be one or both of two messes. If the ducts are not well-insulated, warm, moist air from the living space will enter the ducts and water will condense and might drip into the house. The best solution will be to better insulate the ducts because it will also cost less to cool the house in the summer. If the ducts actually leak air and that is where the cold drafts are coming from, the air leaks should be sealed for the Summer economy as well.

As I understand the situation, you can vent the space between the rafter insulation (fiberglass, cellulose, etc.) and the underside of the roof sheathing (using baffles) and add soffit vents OR you can spray foam insulation between the rafters and close off the vents. The option you suggest would not meet any building code I am aware of. I either case it would be best to insulate the full length of the rafters rather than the knee walls.

Hi. Couple of things: Is this a very old house, i.e., had joined, minimal struture, no consideratin of insulation requirements...? 1. All appliances, bathrooms, sources of moisture MUST be mechanically vented, period, and vented outside, not to attics or eaves. This is critical! 2. The attic space must have a way in for the air or the fan will suck the moist house air through it, to condense on the roof and rafters; 3. Check for roof leaks, bad flashing, just in case this is a bad roof issue; 4. The side roof/walls (top of the gambrel) are too thin for good insulation, and are not moisture resistant or vented. If the insulation is fiberglass, it must be vented or extremely well sealed (almost impossible), especially at a bathroom (see #1); 5. You may well have to take extreme measures. Based on your description, I would suggest removing the interior wall/celing finishes and the now-wet insulation and using a closed cell spray foam insulation. This is impermeable, will not pass moisture and will exceed any r-value of other products. This may seem extreme (it is) but the moisture, mold and rot will do it for you if you don't. Please note that the roof sheathing must be inspected and replaced if rotted; 6. The earlier suggestion of drilling the 2x6 "mid-ridge" might help if the bottom of the eaves can get a soffit vent like a circular vent in each rafter bay or continuous strip vent installed, and if the insulated upper portions have a channel between the insulation and roof sheating and the main ridge can get a vent (or perhaps a small gable vent with a fan if there is a small attic space at the ridge. But this puts you into step 5 for a better result. Good luck. This is extremely serious (as I am sure you know)and will be a lot of work to fix right. But if you do it well, your energy costs will drop, and your roof won't rot away. Also, if your recessed lights are going into unconditioned space like the attic floor, they must be air-tight and insulated cans, not standard units.

"is it worth it to get a vented hood? Would it the cost and hassle be worth it or should we just get some sort of non vented hood?" In my experience a non-vented hood will catch some of the grease that is carried by the hot air that is pulled through your filter but it will do nothing for smoke. Catching some of the grease is better than nothing but only you can decide whether that meets your needs. I Depending on where you live, current code may also require you to vent outside. Though that probably would not apply to you until you did more involved renovations that required a building permit. Any chance that you can use your $700 budget to buy a vented hood that matches the style of your kitchen and you DIY the installation?