I had this problem when I got a new e-distributor for my 64 slant off e-bay since it was missing the internals. As you found the pickup plate is easy, just $7 at rockauto. I had to swap the baseplate from my points distributor. Fortunately, they appear to be the same between points and electronic distributors.
What engine do you have? If SB or RB, a new "ready-to-run" distributor is only $50 and appears to have a much better pickup design, plus an HEI module.