[Axial]

Update: the issue was a multi-part failure, none of which was a blend door or a vacuum line.

The HVAC Programmer unit was faulty; I caved and replaced with another unit that solved the electronic controls locking up but did not solve the frequent, random mode switching.

I discovered that the compressor had a cracked shaft seal; I replaced the compressor, converted to R134a, and the mode switching was dramatically reduced.

Replaced all of the coil packs and plug wires due to the car running extremely poorly and smelling of gasoline; found one coil with a nice crack going up the side. Car now runs strongly and the HVAC behaves as it should, with the exception of a new refrigerant leak that I need to trace. I will laugh if it's the R134 adapters.

To any who provided some pointers, thanks! Even if it wasn't identifying the issue, springboarding helps think through the problem. My guess is there were some pretty wild voltage or current spikes due to the bad coils and seizing compressor causing giving bad signals to the HVAC electronics, but that's all speculation.