After re-reading your initial post, you are absolutely correct RV Roamer, the thermostat has nothing at all to do with the compressor starting as you described it. It begs the question, however, why only in heat pump mode unless it relates to the ambient temperature? The cycling sounds to me that perhaps the system may be popping an internal thermal breaker because the start winding of the motor continues to draw high current and is not cut off because the motor did not spin up quickly enough. The breaker then cools and resets starting the cycle again. (Not sure if this is the way these compressors are built though)
In my coach (wired for 50 amps) the RVP basement unit has two compressors and they serve both functions, with both being required in the heat pump mode. It does have an outdoor temperature sensor to prevent starting the heat pump needlessly. Cooling is carried out with one or both as required, depending on conditions. However, this may vary with thermostat model and/or air conditioner model involved. If I were to be connected on a 30a supply, the 2nd compressor is not available and, of course, the heat pump would not function at all.
I offered this information because, in many cases, people don't understand what is actually supposed to take place in their specific system and report all kinds weird things that are perfectly normal. The discussion then gets sidetracked very quickly with complex solutions that may not even apply.
I just find that the RVP manual covers this process rather well if one takes the time to read and understand it. The RVP thermostat for my model is quite complex (much more so than simply off or on) and has been quite problematic (my personal experience). This has resulted in some interesting reports on this subject on other forums and which will sometimes defy analysis unless the understanding is there.
You appear to have analyzed and understood your specific problem and did not need this piece of advise.
Alfa 38 5ver (Florida)