Thank the stars for dopey Ebay sellers (sometimes)!
My 3455A was sold as not working because it wasn't reading on the resistance ranges (apparently), I have just tested it after first checking the line voltage selectors, and because I remembered to RTFM, the line frequency selector.... which was set to 60 Hz, not 50. I didn't think that on its own would be the issue, but apparently it must have been as once powered up, and self-test run (not even warm) it was telling me a Vishay .01% 110k resistor was 100.009 - 100.010.
Then I had to turn it off because I thought I smelled magic smoke. I opened it up though, and I can't see any signs.... just really clean, gold-plated loveliness. I didn't find any evidence of smoke release, but I did find a dry solder joint on one of the EL caps inside the shield. I gave it a wiggle and you can feel both too much movement and a vary faint click as the joint opens and closes. Bummer.
Does anyone have a hi-res scan of the service manual? Most of the schematics in the one I found are just too low to see component IDs. I've got an original Operating Instructions manual on order, but I'm not sure that has the full schematics in.
Whichever way I cut it, it looks like a real bargain: Best £100 I ever spent