Well, I'm still not 100% what is going on with aioli and me. I tried again tonight, and used my blender. It's possible
I still didn't get the egg yolk mixture adequately beaten before I started adding the oil ... but I dunno. However, on another BB I got instructions for "rescuing" broken aioli, so rather than throw out my mess I tried the rescue operation and, by golly, it worked! The rescue instructions were to take a fresh egg yolk with a little water and put it in the machine. Start blending as I would if I were starting from scratch again and then drizzle the broken aioli into the new egg yolk in the same way I did with the original olive oil. Worked like a charm. I'd have bet money I'd just find myself throwing out a larger quantity of failed aioli but instead I wound up with a lovely batch. I'm still trying to puzzle this out ... the volume of the single fresh egg yolk was less than the original volume of the two-yolk mixture and yet the blender had no trouble emulsifying the broken aioli into it.
Not sure what to try next time, but at least now I know how to fix it!
Here's a question: I've been putting all of the ingredients (except the oil) into the blender at once and then turning the blender on. Should I be adding things one at a time in a specific order instead? The recipe didn't say to do that but I'm grasping at straws here....