Similar situation. 2 batches of extract & specialty grains (5-6 gal, partial boil in 5 gallon pot). I built a 5 gallon MLT with the intent to start partial mashing and decided to do 3 gallon, all grain, full boil brewing and ferment in a 5 gallon carboy. For me, less beer, more variety and more brewing is ok. That MLT should be able to make big beers at the 3 gallon end of boil volume. Making 5-6 gallons would be a significant equipment investment and relocation out of the kitchen.
Here are upgrades that will keep your mash temp to 1F drop in 60 minutes:
Preheat with water 15F more than what you need to get your grain to your mash temp for about 30 minutes. Overshoot your temperature and stir to cool a few degrees to the desired mash temp.
Wrap the cooler in a blanket.
Use spray foam inside the hollow lid.
Cut a styrofoam disk the same diameter as your cooler and put it in a food grade bag (turkey cooking bag) to reduce your air space above the mash. Use R5-R10 (1"-2") thick styrofoam. You can probably skip the spray foam inside the lid if you do this step because no heat will get past this. I throw away the turkey bag or crock pot liner after each use and the styrofoam stays clean and dry.