The engine's now running at 1200 RPM and higher (although it obviously isn't timed properly yet) but as soon as I let off the throttle it shuts down like the key turned off. Sometimes I can 'catch' it by opening the throttle again, but it just won't idle under about 1200.

I suspect the carburetor idle circuit on my rebuilt Carter AFB. I've got the idle air screw dialed out 1/2 turn and the idle mixture screws dialed out 1 turn each per the manual. Any suggestions on what directions to take these screws? I'm putting a lot of miles on my new starter!

Or is the problem somewhere else?

Check for a vacuum line off somewhere. Also recheck mounting bolts/nuts.