It's always something with old cars...
Apparently I have a fuel line blockage to end all other fuel line blockages.
I pulled the line from the tank to the pump, which if directed down will normally siphon gas out of the tank on its own. After it emptied, no more gas followed. I tried some other tricks to get it going-I don't have my Mightyvac handy, but tried removing the gas cap and blowing in it. I got a lot of resistance to doing that, but every time I did it I got a trickle of gasoline out of the line.
With that in mind, I thought maybe the intake in the tank was blocked. Since I couldn't seem to flush it out, I thought I'd try going the other way and pushing it back out the tank. I blew compressed air up the line, and sure enough that seemed to clear it as I could hear gasoline gurgling in the tank and feel air coming out the filler neck. Initially, I couldn't get any fuel to flow back out, but it occurred to me that the side I'd jacked up was where the pick-up is located. Once I'd dropped it back down, fuel flowed out of the tank again.
It seems, though, that whatever was in the line managed to migrate through the pump and into the line running to the carbs. With the pump "primed" again, it would quit running but I'm not getting any fuel flow out the fuel line under the hood. At one point this evening, I'd also running compressed air from under the hood back through the line, but seemingly ended up with nothing but a bunch of back pressure from the line.
So, tomorrow evening, I'll pull the line off the fuel pump then crank the pressure on the compressor WAY up. Hopefully I can clean out whatever is blocking it.