Why are we discussing CG generator allowed hours?
OP, I still see your best option is do nothing. You only want to run gen for a few hours, you rarely use gen.
Propane gens will not have issues with gasoline corrupting the carb because you only run it 20 hours over ten years, s that is a huge plus for you. You will have carb issues if you get a gasoline one.
A TC is so small inside that your AC compressor might run 30 seconds then cycle off for 5-10 minutes, so re-do that calculation of how long gen will run off a tank. 30 secs vs 5 mins is a 10:1 ratio. SO over 10 hours your compressor will run 1 hours (yes, this will vary, but just deal with it until OP gives up exact numbers).
It could run 2 mins for every 5, a 5:2 ratio, do math on that so you have a range.
With just the fan on the AC running you will not be pulling many amps at all and the gen is not using a lot of propane as if under a load.
For my TC i put on a smaller 9200 roof AC unit because it would run off of a small 2200i generator. Quiet, light and easy to carry, plus the inverter gen will idle down when there is no big load.
Consider your camping altitude as the small gens might not have enough power at high elevations to run even small ACs.
Going solar? No, thats just crazy for what you describe as your situation. That would be great for doing a LOT of camping, but just for a few trips a year, use what you got! Spend money elsewhere where it has biger impact on your enjoyment.