[morzh]

Put the bottom of the amp with the transformers into the freezer chest. Will whack it tomorrow.

Also, I followed Arran's advice and re-soldered the filament pins on those tubes that had bad filaments (3) and the P/G pins of the two that have good filaments.
No change.
The good filament tubes still have exactly zero plate current (the needle tries to move 1/3 of one division, which is the same as if it didn't move at all), and the other three never regained the filamet glow.

So, yes, failed tubes, not the solder in the pins.