I was also thinking of using three toggle switches across the front panel
for filaments, plates, and screens, arranged so as to reflect the order in
which to apply the power. I suppose some sort of relay or other device
could be used to make sure the screens never got power before or in place of
the plates. It is a good idea about the interlocks on the chassis too - I
know nobody else will be using this amp besides me but still always a good
idea to design in the safety.
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Instead of having 3 separate switches ,go for a single manual switch , a
sequential timer or separate timers and have 3 front panel lights for
filaments ,anodes and screen voltages. With 3 separate switches you
might operate these in the wrong sequence. With the 3 lights to come on
sequentially you quickly can detect any possible sequential switching
problems.

Frank GM0CSZ / KN6WH