Six years later...
I pulled this sad piece of junk off the shelf in my garage (oh yeah, I have a garage again so I can play with these things), and decided to replace the capacitor inside just for laughs. I'd already tried everything else, so why not. I thought its only purpose was as a transient suppressor of sorts to extend the life of the switching contacts... How wrong I was.
The original cap is .25µF, 1000V. I don't have one on hand, so I grabbed a .33uF 275V cap rated for across-the-line service. After soldering it in temporarily, I braced myself and ever-so-lightly touched the plug to the outlet contacts.
:O :O :O OH! So THAT'S what it's supposed to do! I gave it just a short blast in the garage, and it was just a little bit loud.
I guess the cap was bad.Now off to Surplus Gizmos tomorrow to locate a capacitor with a higher voltage rating. 275V might be fine, but I expect some nasty spikes from the inductive reactance of the coil, so I'd feel better if there was a greater safety margin.
So yeah, this case is closed.