Colin, the key to keeping an ammonia-absorption refrigerator
working at peak efficiency is air circulation. If the hot air can't vent out the top, adequate cool air can't carry off the heat where it needs to.
The standard two-vent side vents on a small trailer are adequate until it gets hot. Many of the later model trailers now have a single side vent with the exhaust through a vent in the roof of the trailer. That's a much more efficient method of using the natural convection properties of hot air.
The posters above have hit on an idea that makes a lot of sense; adding a small fan to help move the air over the tubing on the back of the fridge. I've seen them installed where they blow onto the tubing, and I've seen them as exhaust fans in the upper vent to help pull the hot air out and suck cool air over the tubes. They both work very well to help the fridge to cool when the ambient air temp is high.
FWIW, none of the fridges work as well with the electric heating element as they do with gas, but they should all be perfectly adequate on 120v AC with a little help from a fan.
If you've installed something other than the standard ammonia absorption fridge, then you're kind of on your own... I doubt there are many folks here who have anything but either a standard dorm-style 120v AC unit, or the standard ammonia absorption fridges from Dometic or Norcold. You mentioned that you have a compressor or something that cycles... and ammonia absorption fridges don't have anything but a heating element and are absolutely silent when they run.
Good luck, and tell us what you figured ought!