When air gap is marginal- just hitting a bump, slamming hood can jarrr the clutch into action...so you may be on the ragged edge- of running, not running....

It can shut off due to normal cycling, but not come back on until next highway bump......

Next time it is blowing hot and it should be cool-- stop, pull over, keep engine and a/c running, pop hood, look at front of compressor- is it turning? If not, bump it with a wooden hammer handle. If it engages, starts running, you have an air gap issue, that is too wide. Does it normally cool when ...

What is your suction pressure (low side)? - you have a high mount HT-6 compressor I assume, that may have imploded suction reeds- does compressor turn really easy (engine off) with one finger- with little catches as it rotates? If suction pressure is above 50 psi - you have compressor issues..

clutches are programmed (GM anyway) to cut off at 10.5 system volts to save the engine from stalling- give it reserve battery power when losing voltage- as in a bad alternator. So 11 volts to the clutch won't cause your slipping issue- clutches don't slip until about 7 volts or so-- been there done ...

With Variable stroke compressors- you put the oil in the drain bolt hole- on the belly of the compressor-- they have a crankcase that holds 3 ounces at any given time when running-- you can put the full amount in the crankcase, just that it will level out to 3 ounces as it runs..

sounds like air in the system from here-- did you pull adequate vacuum?

About 12 minutes....

The few I have had- it was always the amp under the dash- replace it..and be cool...scrapyard ones are cheap and work.

Ditto: Sweating only occurs beyond any expansion devices- on low side, not in front of them as is a receiver/drier (RD) which is on high side

Check the resistance on clutch coil- probably a dead short-- meaning bad coil, the coil can be replaced seperately, you mechanic has a boat payment to make, and wants you to fund it...