I know it has been several months, but I thought I would share the conclusion to this tale. Once I realized the problem was with the front tank, I switched to the rear, and have just been too busy until this weekend to deal with it. I did manage to run the front tank completely dry by running it until it misbehaved, and then switching to the rear tan, but I never managed to get it to consistently misbehave or do it where I could get a good test.

I pulled the front pump out, and found the strainer to be strangely colored with some sort of sticky substance. (I also found one wire splice that was not good, but I think that only showed up when I struggled to get the pump assembly out of the tank.) I cleaned it, put things back together, and all seems to be well. This is entirely my fault, and I will never do this again -- I had poured some old 2-cycle gas-oil (from my boat) in the tank thinking a small amount diluted would not be a problem, but it seems to have formed some sticky goo that stuck to the fuel pump strainer. It is really strange because I had filled the tank fully, and still this stuff did not dissolve.

So, once again I provide the example of what not to do. I'm not sure there is a way to fix stupid, but spending several hours fixing things might help!