Well, I thought I'd give a final update of sorts here.
After waiting a day for my sloppy silver pen redraw of the broken lead to dry, I again tested with the ammeter. The connection had definitely been re-established, but it showed noticeably higher resistance than the standard white leads. I didn't know if that mattered, but there was one way to find out. I reassembled the board (stopping halfway and starting over because I forgot to put the spacers back in) and popped all the keys back in. Then, the moment of truth...
I carried the keyboard fresh out of surgery and plugged it back in to the computer. The green lights flashed. So far so good. With bated breath and slightly sweaty palms, I opened a notepad window and slowly put my hands on the board. I typed a simple word using keys I knew worked...success...then I gulped a bit. I slowly reached my thumb for the space bar...the space bar that had months ago stopped working and had been the first sign of something ailing my monolith of a model M. Not unlike the steps in firing a gun, I held my breath and pushed down until it clicked...
...how did it turn out? Well, which board do you think I used to type this post?

I will add a couple of notes here, though: The residue on the clear part of the membrane did seem to indicate that even with the rubbery layer between the steel plate and the membranes, something was able to seep through. I don't know if it was moisture or what, but I'm willing to bet that's what caused that lead to die.
Also, to clean off most of the surface rust on the steel plate, I used a mix of baking soda and vinegar to make a watery paste, put it on the rust spots, let it sit for a few minutes, and then sanded it off with 300 grit sandpaper. For the really light spots, a bit of WD-40 with that same sandpaper worked just fine. After both of those, the surface was still marred in the spots where the worst rust was, but the rust had been cleaned off.
Many thanks to all for the ideas and insights. I had never attempted something like this before and having even a bit of support helped a lot. Here's to happily clicking away into the wee hours of the morning. Cheers!