Surprised to hear that about Royal. They are usually very helpful.
On to your question....From what you are saying you are correct in questioning of your compressor is good or not. Couple of things though.
1) The Royal Milk Machine used to use a manual thermostat and not the electronic one. If you are playing around with those settings it won't change a thing. Try adjusting the manual thermostat colder.
2)When the compressor turns off. does the compressor fan stay running? If yes, the compressor is going out on overload. If no, then the thermostat is shutting off the compressor assembly. (the fan and compressor are hooked up in a parallel circuit)
3) A refer system should pull well below freezing while running. A 32 degree temp is not cold enough to keep your product cold. The best way to test it is this. Plug the compressor into an outlet using an extension cord. Let it run for at least 15 minute. Look at the evaporator, it should be frosty all they way across. If it is frosty on the left only (Dixie is on the right) by the small copper tube going into the evaporator your unit is low on gas.
Now, if you are using this for soda only and nothing perishable you should try to eliminate the health control as it will be more trouble then it is worth. Soda can be run at 45 degrees but that won;t keep the health control happy. I'll have to dig and see if I have a manual or notes to see if this is possible.