Logic suggests that if your generator started one 15K A/C it should start another that's configured the same way.
The ultimate "start" is Micro Air. Below that, there are Start Kits - Capacitors controlled with PTCR, Potential Relay, or Electronic Switching.
I'd try $10-$50 on a Start Kit before $300 on Micro Air or $3000 on a new Generator.
But I gotta ask:
1. Do you know if your old A/C had a Start Kit and the new A/C doesn't?
2. Does your new Camper have so many more Bells and Whistles, that your generator's output is being soaked up by loads it didn't have before?