Try to post a pic from the top with the cap off so we can see what we are dealing with because I still believe the trouble is a broken wire between the two plates causing it to lose ground when the advance is pulled.
I tend to agree. I pulled one of those distributors off of a car in 1975 & the ground wire between the two plates was in poor shape even way back then. Don't know what the mileage was on the car but I'd imagine most of what you find now days has more.