The battery was failing. Would go from 50% capacity to shut down.
The opening was much easier than the closing. Replacing the tiny screws with the magnetized screwdriver was maddening. I would seat a screw in place, but as I got close to the head with the screwdriver, it would suck it out the socket and I would be back again to square one. I was able to replace the battery cover, but was never able to put a cover over the cables on the top right. I sealed up the case without the cover, and the phone is working just fine.
Make sure to keep careful track of which tiny screw goes where. Keep a clear picture of what the cable cover looks like before unscrewing it. An extra pair of hands or a rig to hold the cover at 90 degrees during reassembly would be helpful. Also, a non magnetized #00 phillips head screwdriver might work better for reassembly.