[Arran]

I didn't notice this before, but the diagram shows the Chinese 6P3P drawn as a power pentode, not as a beam power tube. So is the 6P3P actually the same as a 6P3P/6L6G, and the diagram drawn incorrectly, or is it a Chinese version of a 6F6? I also noticed that the 6P3P is self biased, sometimes called cathode biased, so there is some flexibility in terms of swapping tubes.
  As for a shorted Zener diode causing the output to clip, I don't really know why, if you look at the average tube amp they usually take the screen grid voltage right after the second filter cap in the power supply, and have one leg of the output transformer primary connected to the same, the other leg being connected to the plate side. So in those cases the screen grid voltage is usually higher then the plate voltage, and I never noticed anything odd about the audio in those cases. To me it would have made more sense building a fixed bias supply with Zeners then a screen grid supply with Zeners, but then again the amps I'm thinking of didn't use a twin triode for a 1st audio stage with that cathode follower setup. 
Regards
Arran