On to part 2 of this saga: Upon inspection, it turned out that the lamp socket (ceramic) was broken. I removed the "lid" that it hangs in to show my neighbor, who's a retired electrician, and ask if he thought it might be a standard part I could still find. He says, hmm, dunno, but I think I have an old enlarger for you... My son-in-law's been trying to sell it at our annual yard sale for a couple of years now, it's just taking up space in the barn. Come back tomorrow.
So, I now have a compact enlarger, too. It's labeled Lentar L35, but I can't seem to find much info about those. Probably the kind of thing that was sold under many names. I'm looking at enlargers on the 'bay right now but haven't found one yet that looks like it.
It came with a 50/5.6 lens, one 35mm carrier, a 4-in-1 easel, and yet another tank. The slot for the filter drawer is empty, though. Maybe more stuff will turn up once I get a hold of son-in-law himself.
Anyway, this should be a much more manageable setup. The Beseler would only fit on top of the tub, blocking access to the trays below, but this one I can set up on the vanity or a small table.