Generator Woes

It looks like I miscalculated on the 2400 watt Yamaha generator I bought for the camper. It was able to start up the AC with a big moan (from the AC) but as the day wore on and temperatures got into the 90's, it just didn't have enough kick to get the compressor started. I read various camper forums and internet BS artists to see what fix I could do. Installing a boost capacitor in the AC appeared to be a possible solution according to some posts. I wonder why they don't have them in there to begin with. Maybe because most campers are used in the eastern states at low elevation. I ordered a Supco SPP6E capacitor for $30 and followed the installation instructions, including to carefully discharge the AC capacitor by shorting out the terminals with a screwdriver being careful to not touch the metal part of the screwdriver and being prepared for a fairly "abrupt pop". I was shaking during this procedure but the result was very anticlimactic. Today's testing resulted in fairly good results - the AC ran through several cycles without tripping the generator breaker. So, a 2400-watt generator can run a 13,500 BTU air conditioner through multiple cooling cycles at 5000 feet elevation and 85-degree ambient temperature, if one installs a booster capacitor. I shall test higher temps and elevations later.