Let's start at the beginning.

Why are you chasing the monovalve?

My personal belief is that the monovalve has no bearing on the situation. The hot air that you feel when starting the vehicle is perfectly normal. The heater box gets significantly hotter than the cabin. I've noticed this on the SDL. Don't even bother to turn the system on unless the a/c is working. Better to just roll the windows down.

The symptoms of cold air for a short period of time and then gradually warming will be due to one of two general possibilities:

1) The compressor drops off line (a multitude of possibilities, all electrical)

2) The compressor remains on line (engaged) and there is not enough fluid in the system to do the job.

To go further, one of the above needs to be confirmed.

This can be done in the driveway. Set the temperature dial all the way to the cold stop. Operate the system at 1500 rpm and observe the compressor. It should remain engaged for the entire period of the test.