A sad update :-(
First I wanted to say thank you so much to everyone who has tried to help me. However, I must regretfully report that this is not going to be a salvageable Macintosh after all. The corrosion to the analog board was far more severe than I had originally thought. Several components were loose, and many of the traces and pads are falling off the board. But the final nail came when I discovered a bent pin on the back of the CRT. In my clumsy attempt to bend it back into shape the tube cracked and a piece of glass broke off, rendering any potential repairs to the analog board meaningless. Maybe I'll come back to this someday. But for right now, it's a parts-machine.
Its case and most of its innards are still in decent shape, so I'll probably salvage them for other computers.
I still have an SE with a single failed capacitor on its analog board, along with a bad hard drive. So now that computer will be able to live on instead.
I haven't decided what to do with its floppy drive yet. I still have my LC III that I'm repairing (I temporarily gave its drive to an SE for the moment), and the drives on my Mac II are a little mismatched. So either would be a good candidate for a transplant.
The motherboard could be perfectly fine for all I know. I did recap and clean it. Unfortunately, however, I have no way to test my work at the moment.
As for the case, the upper center crew hole is completely shattered on the front part. It looks to be some sort of corrosive damage that discolored the screw as well. But structurally, and cosmetically, it should still be salvageable. The back is a little yellowed and has a few scuffs, but is otherwise in good shape. Who knows, maybe I'll find another beat-up old classic that could use a facelift. Or I'll just sell the bits I don't use on eBay...
All and all, this has been kind of a sad day for me. I was really looking forward to getting this old Classic up and running again.