On an 2002 Coleman TT, I had a 15000 BTU AC. The book said I would need a 5500 watt generator to kick it over. I found that there was a Hard Start Kit for the generator. It was a capacitor that I installed myself.
So, I would inquire if your AC has such an upgrade. The kit only cost about $30. Today, maybe such a kit would cost $50. Talk with service at RV Parts and Accessories for Sale - PPL Motor Homes
They mailed mine to me.
I successfully was able to run the AC with a Honda 3000 genny. Easily started the AC with the kit installed.