Fascinating!!
I'd be very interested in knowing a few things about the "fix" you've accomplished.
First, you mentioned that in installing your own cable, you have bypassed the thermal protection switch... are you sure that this switch wasn't behind the "hot compressor disengage" problem?
Second, you said that even with voltage on the connector, that the compressor would disengage, and that touching your own lead to the battery would cause the compressor the re-engage. That's a bit confusing.... when the car is running, the actual voltage at the battery isn't nominal battery voltage, but is the voltage that is put out by the voltage regulator. This will run somewhere between 13.6 and 14.4 volts. Do you know what the exact voltage is on the plug when the compressor disengages?
If the voltage being supplied to the compressor clutch is low for any reason, (poor wiring connections, faulty connector, burned contacts in the compressor relay, pitted contacts on the over-temp sensor, etc.), the result will be high resistance in the circuit, voltage drop across the contact in question, and reduced voltage to the clutch.
There is also the phenomenon called "hysteresis". Basically, it should require more current through the electromagnetic clutch in order to engage it, than is required to hold it in once it has engaged, due to the fact the air gap has been closed. As the temperature rises, the resistance of the clutch windings goes up, and the current therefor goes down. As the current goes down, the electromagnetic force holding the clutch in weakens, (current and magnetic force are proportional) and the clutch may release. I'm wondering if the clutch is badly worn, or if the initial gap is too large.
Not that your "fix" isn't a good one.... in fact I'm impressed by your ingenuity.... I'm just trying to figure out exactly what is happening.
By the way, have you read this?..... http://au.geocities.com/ozbrick850/aircon-keithP.html

Marty
'96 855T