The following advice applies only if you have determined that the Compressor is running, and that the Blower is not, despite doing every possible switch setting. If I have understood everything you have written, the actual symptom is that the Blower stops completely after running at full steam for about five minutes, and that you have cool air up until that time, and that if the Blower were running, you would have cool air?
Like I said, a full speed Blower is caused by the Power Transistor fully conducting. Usually, it is a shorted transistor, but could be a full speed signal from the CCU. Also, a shorted transistor doesn't usually unshort itself, but is shorted forever, and you have tried a replacement.
Sorry that I don't have the wiring diagram with me, so you will need to get one to know what color wires to use for measuring the voltages. You will have to measure voltages when the problem is occuring. A 12-volt reading across the Blower power leads indicates that the Blower should be going full speed. A zero volt, or near zero volts reading indicates that the Power Transistor is not conducting. A possiblity with a 12-volt reading is that the Blower Motor winding is open, but does not indicate how it could keep repairing itself with each cooldown. You will need to measure the resistance of the motor's winding to determine if it is open, or an infinity ohms reading at the time of the failure.
Also, measure between chassis ground and the + power lead of the Blower. It should read 12 volts, or thereabout, when you are running the A/C. I can't believe this is bad, but just check.
Now, if there is 12 volts across the Blower, and it is not running, the Blower would be suspect. Zero volts, or near zero volts across the Power Transistor indicates it is fully conducting, and the Blower should be going full speed. If you read around 12 volts across the Power Transistor, collector to emitter, then the Power Transistor is open (not conducting) at this time. If there is some voltage on the 3rd lead of the Power Transistor,(base)then the CCU is probably trying to control the Blower.
Everything said, I am leaning toward a bad CCU, but I am not there, and you are, so you will have to figure it out. I am afraid you do not have the expertise to handle the steps I have given here (no insult intended), but maybe someone can help you. You need a good multimeter, the wiring diagram, and the ability to understand the diagram and the voltage readings. I would test the Blower with the battery voltage, and the Power Transistor with the meter, and force the Power Transistor to conduct with another small adjustable voltage source feeding the base lead. If I could eliminate those items as problems, then I would see if I could get a used CCU to try out. You could, of course, try and force the Blower to run with another voltage source, and if the Compressor runs like you say, the cold air would be back.
Sorry, but there is no pat answer for your problem. It just has to be tracked down. Good luck.
Regards,
Bill