That was going to be my next 'best guess', the protection circuit is shutting the HV down prematurely but that wouldn't account for the supply line dropping as the load increases. The protection circuit drains the bias from the HV oscillator which would tend to reduce it's current consumption so there would be less load on the supply. I would anticipate the supply voltage rising to compensate for the extra load until the oscillator was shut down, the opposite seems to be happening. Besides, if the protection circuit operated, I would expect the overload monitor (lamp/LED?) to indicate a fault.
Agoo, try this:
MOMENTARILY short out the base and emitter of Q15 and see how it changes operation. Do not leave it running for long with the short in place as it could overload the HV oscillator transistors. I think it's Q15, the schematic is too blurred to be sure but it's the one in the extreme bottom right corner of the HV.jpg image you posted.
Brian.