My Messicks order showed up much sooner than expected, so I was able to install a new throttle cable, which has cleared up most of the remaining quirks, and taken the guesswork out of where to set the throttle on startup. With this new part and some more time spent on learning to purge the system, the old girl is now starting and running pretty reliably.
For grins, I picked up a shiny new throttle knob that won't keep falling off, plus I went ahead and replaced the plastic bowl that holds the paper filter/element just before the injector pump. The old one was still serviceable, but was really yellowed and seemed to be getting brittle. You just know it would have decided to crack apart over a weekend, bringing the machine down. I installed the new one, and set the old one aside as a spare.