[morzh]

Today put the tuning cap back, this time not having forgotten to solder the GND lead to one of the bottom bolts.

Checked the transformer outputs; seem fine, 700V more or less.
Checked the rectifier output for shorts; OK.

Put the tubes back, checked the pilot lamp; no light. Popped out, Deoxited the holder; now it glows.
Put the rectifier back (speaker has been connected all this time), put the Variac to 70V, saw the DV rising, and quickly dropping after the turn-off: a good sign.
Then put the Variac to 110V, see about 430V DC, dropping to 280V or so, then the speaker came alive; put the tuning cap to about where the local station should be (no antenna, and all is being done in the basement), and the station came nice, loud and clear.
Put my finger to the Antenna clip, went through the BC band - nice reception across the dial. No hum either.

So, I will see about those mica sheets, but if it aligns well without the replacement, so be it.
Alignment tonight.