UPDATE: Fixed - maybe!
I swapped the fuel line to draw from the other engine's pickup - bled for a while (OK, a long while), and got it started. Let it run at least 20 minutes w/o issue. Then let it sit for two days - since sitting has always revealed the problem. Started and ran - a little rough in the first 20 seconds or so, then ran fine. Let it run at least 10 minutes w/o issue. Then let it sit for two more days - and today, it started, was a little rough in the first 20 seconds - and then ran like a champ.
Is it fixed? Maybe. Hopefully. I say that because I have now pulled the "suspect" pickup tube up out of the tank as far as I can (can't remove it completely because the engine room ceiling is too low), and I didn't see a single thing wrong with it. It's solid steel welded to the bottom of a steel pipe elbow, and the welds look solid, and the pipe does, too.
After today's successful start, I added a "T" to the fuel line to the genset, and hooked the good engine to it, and made sure they'll both run from the same supply, which they do. That's how I'm going to leave it for a while. Until the problem occurs again (and then the new lift pump goes in), or until after the impending trip down to the Keys (when I think I'll put the new lift pump in, just because I know the old one is pretty old).
So what's the lesson? Perseverance, I guess. And that sometimes, even if you get something fixed, you don't really know what was wrong - and I can live with that.