"The screen voltage will come up to normal after sitting over night, 400 V or so. After approximately 5 minutes or slightly longer, I hear a slight arcing. From that point on, the screen voltage will wander anywhere from 75 V up to maybe 150 V. Adjustment of the screen control on the flyback has only a small effect and is not permanent. Removing the CRT pcb results in the screen voltage returning to normal."
This is very likely a short between electrodes inside the CRT unless there is something on the neck board that is breaking down as a result of some connection to the CRT. The flyback should largely not know the difference with the socket plugged into the CRT. However, on rare occasions, there is contamination within the 'plastic alignment base' on the end of the CRT neck. (It is possible to CAREFULLY remove the plastic piece and clean the CRT glass/pins. Reinstall the plastic piece if it is still intact or leave it off - just take care in replacing the CRT neck board.)
One possibility is that glue used to hold components down on some circuit boards has deteriorated and turned conductive. Check for tan to brown stuff shorting traces on the CRT neck board. If this is present on the focus or screen traces or wires, it may just be your problem. Scrape off all of the old glue and then clean thoroughly. Repair any damaged traces.
What happens to the HV? A HV breakdown possibly inside the CRT would result in all the voltages being dragged down.
What happens to the picture?
If you connect a charged HV capacitor (guessing a couple hundred volts, a couple microfarads) between G2 and G1 or focus, you WILL know if tapping the neck results in a momentary short! I cannot predict whether this will be a temporary cure or permanent killer. See the section: Rescuing a shorted CRT.
Here is another thing to try: put a 100 M ohm or so resistor between SCREEN and the CRT socket. This should not affect the behavior much until the failure occurs. Then, check the voltage on both sides with a high impedance voltmeter (1000 M). If the CRT is arcing, it will be much lower on the CRT side and will probably fluctuate. You can play similar games with focus voltage.