Given the changes in coupling but still seeing the issue really leads me to believe it’s power supply related. Another indicator of a PS issue is both channels oscillate in sync--but were both channels loaded identically on their outputs, or did you excite only the loaded channel while leaving the other channel unloaded?
If it’s still happening when feeding a signal directly into the power amp gain stage then there’s not a whole lot more to check to isolate it. Some additional things to try:
Remove voltage amp tube from power amp section and retest (driving the amp from the grid of the inverter tube).
Remove voltage amp and inverter tubes from power amp section and retest (driving the amp from the grid of one of the output tubes)
Reinstall gain and inverter tubes but remove feedback (temporarily) and retest (driving the amp from the grid of the voltage gain stage--careful! amp will be super sensitive w/o feedback).
Try clipping in a smallish (say 22 uF/450V) cap in parallel with one cap in the PS at a time, but ensure the clipped in cap has a solid ground connection on the "noisy" end of the ground bus and retest by driving grid of voltage amp directly. Careful with paralleling that cap with the upper cap in the PS doubler. It's negative terminal is not at ground potential, so the clipped in cap should go from the pos terminal of that cap to the other side of the secondary. This test is simply verifying each PS cap is working correctly and has a solid ground connection. If one of the caps has a bad ground it's effectively out of the circuit.
There might be a few more tests you could conger up to try to isolate which stage is causing the issue....
Also stupid question but I gotta ask. Is the positive feedback between first and second power amp stages connected correctly with the correct resistor values? Here:

If it’s still happening when feeding a signal directly into the power amp gain stage then there’s not a whole lot more to check to isolate it. Some additional things to try:
Remove voltage amp tube from power amp section and retest (driving the amp from the grid of the inverter tube).
Remove voltage amp and inverter tubes from power amp section and retest (driving the amp from the grid of one of the output tubes)
Reinstall gain and inverter tubes but remove feedback (temporarily) and retest (driving the amp from the grid of the voltage gain stage--careful! amp will be super sensitive w/o feedback).
Try clipping in a smallish (say 22 uF/450V) cap in parallel with one cap in the PS at a time, but ensure the clipped in cap has a solid ground connection on the "noisy" end of the ground bus and retest by driving grid of voltage amp directly. Careful with paralleling that cap with the upper cap in the PS doubler. It's negative terminal is not at ground potential, so the clipped in cap should go from the pos terminal of that cap to the other side of the secondary. This test is simply verifying each PS cap is working correctly and has a solid ground connection. If one of the caps has a bad ground it's effectively out of the circuit.
There might be a few more tests you could conger up to try to isolate which stage is causing the issue....
Also stupid question but I gotta ask. Is the positive feedback between first and second power amp stages connected correctly with the correct resistor values? Here:


