[Richard]

Based upon your description, this could be a whole host of different causes, so thanks for being open to collecting data to narrow the diagnosis.

I am pretty sure you have basement SCS units. Would you confirm?
Are you comfortable working in a control box with live electrical circuits?
Do you have a clamp on ammeter?

First let’s talk about what the original tstat is supposed to do. On cool, there is an approximate 3 second delay before the compressors will kick on. If the setpoint is 2 degrees or less than the actual, then only Compressor 1 will activate. If the setpoint is 2 degrees less than actual then both compressors will activate.

If low cool or low fan is selected ONLY one compressor will activate. The primary purpose being to allow you to eek by on a 30 amp service.

Now to collect some data. Turn off the rear unit, no need to confuse the amperage readings with the rear cycling on and off. Turn the front unit on low cool, not low auto and set the target temperature 10 degrees below the actual. Does the inside fan come on ? Look at the ammeters above the driver cockpit and record amperage readings on both before you start the experiment. Now watch the ammeters when the tstat tells the unit to start. Record what happens and the reading. You should see a spike on L1 and then it should settle into the 15 amp range (12 to 15). Let the unit run for 15 minutes in this condition if it will and monitor the amperage reading periodically. Does it remain steady? Decrease? Or Increase? This tells us if it is a stopped up expansion valve or potentially low refrigerant. 

When that is complete after 15 minutes of run time, without turning the unit off with the selector switch, turn the selector to HI cool , not HI auto. And repeat all the observations including 15 minute run time for a second time. You should see similar behavior for L2 on the ammeters.

This info is going to tell us what is going on with the compressors. The data on air discharge temp is very helpful. Please continue to provide. 

Now pull the cover off the circuit board panel on the front of the AC unit. One screw at the bottom is all it takes, and a hook pick to pull the bottom straight out. Take some pics of the board please. I ask for two reasons. One, it will tell us which board you have, for there a a few generations of them. And if the board is “smoked”, we may be able to see an issue.

We can go further when you report this info.

If you want to guess that it’s a thermostat issue, you can simply swap the front and rear tstats. The wiring is simple, but take a pic just for grins.

But you know me, In God we trust, everybody else bring data.