Some even better news... The variac just had a funky switch, and is working now!
I've done the preliminary non-rectifier tests, and all seems well so far- transformer didn't even get warm, all of the tubes lit up, and both the dial lights lit.
I kept the voltmeter across the filament line, and it's bang on at 6.3v AC.
(the occasional twitch to 6.4, but I expect that's because the wall voltage is 120V as opposed to 117 the set wants.)
I also checked the chassis to ground voltage, there's about 33v AC, so no major shock hazard.
I also probed the HV out from the transformer, that's at about 500V AC.
It seems a little on the high side, but I still live in a silicon world where rectifiers are that efficient
It's getting dark now, so I'll wait until tomorrow to put in the rectifier and do the secondary tests. Pictures of that warm tube glow coming soon!
Edit: Pics posted in the build log. Here's one to get you started...