I'm not really sure what the cause is, but here's a couple of comments:
1) I really don't think the low voltage is a problem at all. Due to the wiring harness resistance, I'm not at all surprised that you're only seeing 11.9v downstream. That should not be enough of a drop to cause the system to fail. If it was under 10v or something, yes, that's bad... but around a nominal 12v, I wouldn't bother spending any more time there.
2) The clutch is probably not slipping... the KLIMA would kill the compressor. It has a tach at the rear of the compressor, and compares the speed to engine speed. All you need to do is make sure the compressor (clutch) is not disengaging above a certain RPM (looks like 3k is the magic number here).
3) The fact that you can physically pinch off the heater hoses and prevent hot coolant from entering the heater core, I think we can rule out anything in there.
4) To check the compressor engagement, you could rig up a test light (small 12v bulb) in the passenger compartment, that turns on when the clutch is engaged. Go for a drive, see if the bulb (compressor) turns off just before the vent temps skyrocket. That would indicate a control problem.
5) Assuming the compressor is staying engaged, the problem appears to be refrigerant related... time to check pressures. If your lines have unmolested Schrader valves, it's likely still an R-12 system (and if so, DO NOT convert it!). If it has adapters screwed on that are "quick connect" type, it's been converted to R-134a... but there should be a decal under the hood indicating this. You can buy gauges (make sure you get the right type, R-12 or R-134a) and do this yourself if you want.
6) I believe there is another electrical safety circuit, separate from the high/low pressure switch, that can turn off the compressor. On the older models it's tied to a temperature switch. On later models it's tied to a temperature sensor. Might be worth investigating this, the sensor could be bad...?
