The Honda 2000is probably the smallest package generator for its power rating on the market..
Going propane because you already have a tank of it, won't work very well... First because propane powered generators have less power than gas one, and second because they go thru propane at a astounding rate.
Much easier to carry a small one gallon container of gas for the Honda which coupled with the gallon it holds would give about 20 hours of run time.... If 10 hours would be enough, then you could leave the extra tank at home.
I wouldn't downsize the microwave too much as some have suggested as then it won't work very well.
Extra batteries, solar, etc. all have drawbacks. Batteries, cost and weight, and when it's drained, you are done. Solar, cost $$ complexity., and it won't work in bad weather.
A small generator will work in any weather, and provide practically limitless power, and not weigh much more than a battery.
If carrying a small gas can is a issue, your TV has a gas tank... Figure out a way to access it. It can be as simple as a siphon hose or as custom as a plumbed in hose, pump etc.