I had a stroke of bad luck or good luck today, depending on how you look at it. I left the keys in the ignition with the ignition on after it stalled. Then I went to make myself a sandwich and forgot about it. When I went back down to the garage I smelled plastic burning. When I went to investigate I found I had burned a hole in the coil:
Autozone was kind enough to replace the coil and cap under warranty since I bought one just a few weeks ago.
I took the opportunity to do a compression test. All six cylinders are reading about 125 PSI dry. I didn't bother doing a wet test because that looked fine to me. My Haynes manual says 130 PSI is the spec, but this is an old engine and I didn't see any cylinders drastically different from the others.
To my surprise, when I put all the plugs back in and put the distributor cap and coil back on, it started right up and ran without stalling.
So, either my previous newly bought coil was bad, or there is a short in the wiring loom somewhere around the spark plugs, because I moved things around and it works now.
The carb is still leaking fuel pretty badly. Rather than attempt to buy new gaskets of higher quality and check all of the specs, I think I'm just going to buy a remanufactured carb. If that stops the fuel leaking and the engine keeps running, I'll call it done and be happy.