When you first use the generator the battery charger is going to pull 5+ amps. There is no reason to wait 15 minutes before trying to start the compressor...30 seconds is long enough. I would try shutting the battery charger/converter off at the 120V circuit breaker and start the AC (your generator is big enough to start just the AC unit) and then turn the charger on. If this doesn’t work then a hard start kit is in your future.
Hopefully by the time the AC cycles off the batteries have been changed enough that the AC will start.
