Hello Mike,
Even before I finished reading your story, I was already thinking along the same line as you: a vacuum leak of the AC701 tube, or a nasty case of filament microphonics may be at the root cause of the high frequency squeal.
You may be able to change the squeal's resonant frequency or its intensity by gently knocking the tube with the handle of a small screw driver while the mic is on. If the squeal indeed changes behavior, this would confirm the tube as the culprit.
And should this be an issue of an oscillating filament inside the tube, there is a sledgehammer cure that sometimes works: give the tube a really hard knock with the screwdriver handle (remember: the next step would be replacement anyway!) Sometimes that knock will reorient the oscillating filament and quiet it down. This cure of course will not work if a vacuum leak is the origin of the squeal.
A side note: I have observed that in many cases where there is an AC 01 with a high level of microphonics, including run-away microphonics, the heater voltage was often set too high.
So make sure to start your testing procedure by correctly calibrating your power supply's tube heater voltage to no more than 4.00VDC, as measured directly at the heater of the tube (not inside the power supply!)
I set the heater voltage for all AC701-powered mics at no more than 3.95VDC, with a minimum of 3.90VDC.