It just occurred to me to try the Carlson's Super Probe on the display. It does use some form of AC signal as I can hear it with the probe, but I must get the probe almost touching the display to pick it up. Every other LCD display in this house I can detect from an inch away or better (my phone almost a foot away).
So we know it isn't DC driven now, which is one huge problem avoided, but maybe there could be a leaky capacitor allowing some DC bias on the display anodes.
Sorry for thinking out loud here, just hoping someone else is travelling the same road.
Edit: or maybe its not a leaky capacitor, but some other mechanism leaving a floating charge on it that does the same. Maybe each anode needs a 4.7MΩ discharge resistor to keep them all at 0vDC. In either case, I think this project will hit a wall, its a lot of anodes and fixing that kind of problem is not going to be practical. Gonna open this thing up after the holidays and see what it looks like