I think I'm finally getting somewhere on this. What do we know now:
1 - The one GL wall unit appears to be somewhat okay running by itself. The controls work and it tries to heat and cool.
2 - The GL unit doesn't, at this point, have the capacity to cool the big room enough.
3 - When two or more of the smaller bedroom units are turned on the "big" GL unit all but stops cooling.
This brings to mind a question. When the GL (24,000 Btu) unit is running alone is it cooling near its capacity? How would we test this? Fortunately the CFM for the 5 different fan speeds are in the service manual. I should have thought of this before... it is easy to calculate the cooling provided (Btu/Hr.) using the very common equation Q=1.08*dtF*CFM. So I tested the unit while on full cooling (min. set point of 61F) at the 5 different fan speeds and this is what I got.
What do you think now?