Alright, back together and polished clean with Novus 2, this gorgeous ereader is ready for another decade.
Screen replacement was, to sum up, a pain in the arse, but the replacement screen looks great and performs just as well as the original.
The replacement battery is just slightly the wrong size, just a hair too thick, so the top and bottom trim pieces don't quite line up properly and I had to use a tiny bit of adhesive tape. eBay has lots of folk selling these just-slightly-too-large batteries. Cameron Sino batteries are the right size, although double the cost. Maybe I'll get some more of the nice batteries.
(I was using Cameron Sino batteries in my Windows Mobile phones back in '09, they're a decent third-party battery factory who've been around for years, not some fly-by-night keymash-name amazon spammer)