Not Getting 12 Volts at Coil

Kudos for taking such a thorough approach to diagnostics., and not that you need "one more opinion" but...

When the car ran for a few seconds, did anything happen to kill it? At this point I would have begun to suspect that the timing had jumped or valves stuck open, compression gone for some reason, etc... except that your diagnostics pointed to a real problem. No spark on some of the wires. That is the most critical item to correct and it was never resolved. It appears the shop is having issues with this also. Did you ever test the old pickup, or put in a new one? (btw a brass feeler gauge is just to keep the gauge from "sticking" to the magnet for ease/accuracy of checking gap). If the pickup is good and the coil has 10+ volts, then the only other animals that could affect "some" of the spark is the distributor (metal trigger star damaged or shaft warped so much that the gap is too wide to trigger on one side and maybe too close on the other), the cap(cracked), the rotor(unlikely if you get spark on at least one wire), or the brain box. If the dizzy is damaged you may have had other internal oh-no's. If you have voltage issues to the coil, you may have issues with feeds too/from the brain as well. I don't know if this could have created the problem you have but it would certainly manifest somehow.

The mechanical "hot wired" distributor approach may circumvent the problem if electrical, and I am sure it would be great to have it running… or at least prove that the problem is elsewhere, but there is still an issue with the electronics that would have to be addressed.

’74 Sport is correct. Use the "process of elimination" approach but be sure you follow each trail to the end, verifying every component in the chain and stating with the most simple and inexpensive items first. You started out on this path with the electronics but may have abandoned it in frustration just as you were closing in on the solution. It may be the shop’s problem now and I hope it doesn’t come back to you broken still, but there is an answer no matter how obscure (or simple) it turns out to be.

I will be waiting for this one’s resolution.