From some of the discussion I am wondering if you considered the possibility that the fan could be the culprit. A fan will run at higher current for a long time before it fails and might be enough to kick it over the edge. I think the cap for it is very cheap and has both start and run in it.
Another thing is - has the condenser coil been cleaned recently? If the compressor has to pump against too high a head pressure, it takes the max of the current to do it. Use some degreaser on it let it sit for awhile and hose it off. You should see an immediate reduction of current on the compressor run.
My Coleman Mach 8232 series rear A/C was always able to start and run at the same time on my Genset 6500 watt. This summer for the first time it refused to continue when the load was placed on it. Come to find out that the compressor was pulling enough to trip a 20 circuit breaker. Rather than work in the sun on the roof, I decided to replace them both. Just to be sure, I replaced all of the capacitors (they were old) and that did not help. So have ordered Atwood 15028 15K btu heatpump units.