Aha! That is an interesting conjecture and experiment. Much appreciated PJ!
I will implement the switch -- and to that end, I have some practical follow-up questions:
(1) Do you have in mind a dead short (section of wire) in parallel with the primary - in which case the primary will still see the voltages of start-up and shut-down transients? Or should the output transformer be completely removed from the path of the transients -- in which case the switch will "switch" between primary and dead short?
(2) I think you've told me before that the output tube doesn't care how it is AC loaded. If that's the case, would it be safe to accidentally send signal through the amp when the output tube has a roughly zero impedance path to ground for signal? I wouldn't deliberately do this, but I might forget one day to flick the switch before hitting "play".
(I should add, further to your point about small signal use with headphones, that for the last while I have put a non-inductive resistor in parallel with each channel at the output, so that the output tube of the Kaiju sees a load close-ish to design spec. And I do almost all my listening with the course attenuator of the BeeQuiet set to -18db, and occasionally -9db for quieter recordings or when really want some thunder. And the Kaiju PEC trimmer pots are fully open (zero attenuation). All of which is to say: by Kaiju standards, the amp produces a fairly large signal to do the demagnetizing. But I am still eager to try the switch experiment, since I would expect changes to signal size to change things by degree not in kind.)
Many thanks again, Derek