I'm not an expert but this is what I would do. Check the amount of charge; is there a sight glass? There should be no bubbles after a few minutes of running. If no sight glass, check with guages.
Does the thermostat cycle the compressor on and off?
Is there a air filter that may be clogged?
If all this is correct, then changing or adjusting the thermosat expansion valve like you did should have solved the problem.
This truck has done this from day one. Everything has been changed, checked, and reverified, except this switch.
Here is what happens. You start running the system and all is well. Air is cold and everything. After an hour or two the air flow is getting restricted (icing up) and eventually the heat transfer to the evaporator is no longer enough to keep the pressure up and the low pressure cutoff switch cuts off the compressor. Large quantities of water drain out. It gets real warm because the low pressure switch has a wide operation band and the TXV is of the type that does not let any through when the compressor is not running.
Well after half an hour or more the low side will rise enough that the switch will allow it to cut back in and it starts to working for some time before it freezes again. Meanwhile it gets to be like a muggy swamp in the cab, or when it happens in winter, it fogs all the windows so bad it is a hazard to vision.
I have worked around it by replacing the factory low pressure switch with a Ford cycling clutch type from a mid 90s truck but it is not a very good solution because that is for a flooded type evaporator with a suction accumulator and it keeps this evaporator too warm for very good cooling on hotter days.
What I really need to know is how to get at the evaporator temperature switch on this unit. It is not apparent at all. Do I go from the cab or engine side? Does anybody have a part number or wire numbers for it?
And sometimes it does work on its own, but only when it feels like it. I recall seeing some sort of a recall on this issue for a T2000 but I don't know if it applies here.