While I can't speak specifically to the 2.2Kw generator running your 19'er A/C, our 10 yr old (330 hrs on the hobbs) EU2000i generator would not start the A/C on our 2018 19'er at 7,000' elevation. (Of course, higher elevations de-rate / de-power internal combustion engines.) So I added an "Easy Start" from Micro-Air. That "fixed it". Now the generator runs the A/C, no problem. There's many great videos on YouTube on how to install the Easy Start. It's not difficult at all.
2018 Escape 19'er & 2018 Highlander
Not all who wander are lost