So I think I may have it sorted out. Don't want to speak too soon though...
I installed an extra fuel filter inline next to the tank.
I also installed a new primary fuel filter and the new fuel sender unit, o-ring and lock ring. I had to re-solder one of the connectors and use the heat gun on the rubber boots to get them soft enough to push over the terminals. I also blew out all the fuel lines with my air compressor turned down to 40-50 psi or so.
Started the car after a bit of cranking to fill the filters, and it seemed to run...OK. Still missing and hunting somewhat, but I got it into a state where I could drive it around the neighborhood. After some more tinkering, it was alright, but then it died again the way it did last week. I coasted into the driveway and pulled the top off the rear carb fuel bowl: Dry as a bone. 😡
Really frustrating, but then I noticed that I forgot to put a hose clamp on the fuel pump inlet line. Also, it was kind of loose. I wonder if the fuel pump had been sucking air, creating a kind of vapor lock condition in the fuel lines? Regardless, I put a clamp on it, and the car seemed to run a lot better. I was able to drive it down the road a little ways and it didn't threaten to die at any time.
I didn't want to get greedy so I came home and decided to wash it. It's the first bath it's had in almost 20 years. The paint cleaned up really well and looks fantastic; the painters did a great job with it. There are a couple of tiny water leaks but nothing major. I don't plan to drive it in the rain anyway.
Current engine bay status:
Yes, that's blue painter's tape protecting the left shock tower from getting scratched by the air filter wingnut.