Break out the champagne -- I got rid of the click! It's not elegant, but it worked.
It looks like someone replaced all the springs at some point, and made new holes for the L ends to fit into. The hole in the pad board for the E/F is too wide, so the spring was moving around. I straightened the long part of the spring (that lies on top of the pad board) and tested it, but it still wiggled around. When I held the spring in place with a screwdriver the key worked smoothly, so I used some 24 gauge copper wire to bind it snug against the post (correct word?), fixed a couple more bushings, and Voila! It might get loose again after some play, but now I know what's up.
Dave Elliot -- your book arrived today and it is already quite useful. Very clearly written -- thanks!
And thanks to everyone for suggestions and information. This is a really nice community.
--carol