"I'd like to find something I can actually "cook" in the pot (i.e., add something to the already boiled water and wait)."
You don't want to cook food in your pot - it's for boiling water. If you do cook in your pot, guess what? Yep, you have to clean it up afterwards - with soap & water.
What you do is bring along whatever food you want to eat, whether it be couscous, pasta, rice, etc, by storing each meal in individual freezer bags. For instance, tortellinis are around 110 cal/oz. If I want to eat 1,000 calories for dinner, I measure out 9 ounces per serving when packing.
Btw, calorie count is very important. Mountain House typically has less, sometimes much less, than 100 cal/oz. So not only are you paying more for a sodium bomb, but you're also carrying more weight per calorie. Also, another nifty trick is to bring along 1-2oz of oil. (Oil is pure fat and avg 250 cal oz.) In the search for high cal/low weight, some people even 'eat' the oil, but a better idea is to pour a little bit on your pasta, rice, etc to beef up the calories.
In order to keep the meal hot while it's sitting/cooking for 10-15 minutes, you simply buy a $1 bubble envelope that is large enough for your freezer bag ie quart and/or gallon size, to fit inside. It operates exactly as a cozy, except it's a little lighter, it doesn't have to be crafted for your pot, and it can be disposed of at the end of your hike.
Be aware that some people think using freezer bags somehow has a larger footprint than disposing of soapy water in the high country. They are wrong. Besides, in the scheme of things, freezer bags are about 1:1,000,000,000+ in order of magnitude compared to simply flying/driving to your chosen destination.