Garage Wiring: No Voltage With a Load
Ok ,you megged it's you know more than most home owners. 

This sounds like a broken conductor. 

With a light load everything works. Add a few amps and the arc separates the wires. You have megged it so you know it is not going to ground. The only other problem that I have seen like this is from "back stabs" or broken conductors. 

With the age of your home I would look for a broken wire in an outlet that daisy chains to the next outlet. 

That or a problem in the panel. 

After reading everything again your Fluke meter may be the problem with "leakage" or "phantom" voltages. I can say this as a profesional that uses many diferent models of fluke meters &amp; meggers. 

Very high impeadance meters will show a normal voltage with no real coper to copper connection. 

Some times  the voltage is from leakage on solid state electronics. Other times I have found moisture &amp; dust enough to cause phantom voltages. Once a load is on the circuit the voltage is gone.