So I did the test that Jerry recommended and the stud that passes through the dist. housing is not grounding out. The test light flashed rapidly on and off when the engine was cranked as it was supposed to. I took the dist. out and discovered that the brand new points I'd installed had come apart in two pieces. The tiny spot welds that were supposed to hold the two halves together failed. Put the old points back in and got the engine to fire up. Had no oil pressure so I know I didn't have the dist. fully seated into the oil pump. Went to address that and am having trouble starting it again but I think it's just a matter of positioning the distributor correctly.
Maybelline, thanks for the pointer on #1 and #6. When I pick it up again tomorrow I'll pull the valve cover off to make sure I've got things right.
Joe, thanks for posting that link. That part looks identical to the one I broke. Might be able to get that version to work.

1956 Chevy 3200