... the diodes do not alter the tone ...
... You want the diodes to have a reverse voltage rating of 3x B+ or more. 1N5408 or 1N4007 are rated for 1000V so they're fine for B+ voltages up to about 330V, but for higher voltages you can use two in series. That's exactly what I have in this prototype amp where my B+ is 470V (the diodes are wired to the ground terminal on my 16ohm winding because that was a convenient tie point for me)
I tried that arrangement (3x1N4007 string per push pull side) on a couple of my amps.
I got a bit suspicious about the tonal impact, so with my old AC30, I put the ground returns of each string on a pole of a dual pole switch.
Thereby allowing a fairly instant AB comparison of the diode / no diode tone.
With an amp used clean, I couldn't detect any difference. But cranked up (into a real speaker, Fluxtone Model 10), switching in the diodes caused a noticeable smoothing of the tone (I think my hearing tops out at about 10kHz).
It's certainly not a night and day difference, but I found it noticeable, and I'm normally the guy that's mystified by people claiming to hear differences in cap / resistor etc brands.
The change in the amp's output waveform was apparent on a scope.
Unfortunately I didn't record any audio or take scope photos.
So it may be worth your while trying a similar AB test

Additionally, when I've checked overdriven output valve anodes with a 100:1 probe, the back emf spikes look to be well over 2kV, so I'm not sure 3kV of diode would be sufficient in the case of, eg a dodgy intermittent connection in the OT secondary circuit (though the back up safety resistor might mitigate that).