Timmy and I have been in contact over the phone.
I believe he has the flyback hooked up right.
A test was done with a known good 6BK4 as follows:
bad set 6BK4 installed in known working set, Known working set exhibits the same problems so the 6BK4 is causing the problem
Known good 6BK4 is installed in Bad set, 6BK4 quickly appears to short out around the filament leads. Tube is tested by retrying in known working set, confirmed prior good tube is toast.
So we concluded the regulator tube is the issue AND the bad set seems to be creating bad tubes from good tubes.
http://scottbecker.net/tube/sheets/137/6/6BK4.pdf
Timmy is going to check the HK voltage potential to see if it is exceeding 225v per the data sheet. I am thinking a problem with the voltage divider resistors (180k/150k) off the B+ that is used to float the shunt heater upwards to prevent insulation breakdown around the heater.
Timmy will 1st check the known working set pins 1 and 2 of the 6bk4 socket (HK) voltage and then compare to the bad set. I advised him to simply disable the HV for now by pulling the horz out while testing. remove the 6bk4 and read the voltages right a the socket.
I would also like Timmy to check voltage pin 1 to ground (shunt cathode) and pin 2 to ground (shunt filament). again the difference in the two voltages should be less than 225vdc
If there is a problem, I would guess the 180k side of the voltage divider (filament to B+) may have opened up or drifted up dropping the DC voltage on the filament.