Generator to Run 15K AC + Residential Fridge In a TT?

TT in question is a large 2-slide with 15K air. This spring I replaced the failed Dometic OEM with an 8 cubic foot residential fridge, and have been happy with it. Everything stays cool for the distances I am driving. However, I want a generator to pair with the fridge on the rare occasion I am towing the unit for a day or more. I am thinking it might be prudent to have one that will run both the AC and the fridge when there is no shore power.

I have doubts that either the Honda or Yamaha combos will be enough. Looks like you have to go all the way to 5500W to do much better, there doesn't seem to be much available in between.

Anyone have any experience with this set up, or recommendations?