First Thing First
Brother of The Benz, Jeep Boy
As Larry replied, if your tech can't figure this one out, change techs.
If you were able to install 3 cans of freon, the compressors suction MUST be operating.
As how to tell if it is, you have a manifold gauge set that you used to charge the R-12 system.
You say you have a GM type compressor?
Does it have service valves?
If yes, you don't have to clamp the low pressure hose, just close the suction side service valve and see how much suction it has(inches of hg.)
Now you plan on converting to R-134A?
If it won't cool with R-12, it won't with R-134A.
You need to do some serious trouble shooting and keep notes and/or get some experienced help.
Happy Trails Beep Beep from The Spiderman in Houston!!!