Alright, I have a probable answer. I took the watch apart again, and the connector from Step 4 wasn't seated properly. 🤦 When I reassembled the watch the first time, I thought that maybe, since they lined up when I put the two halves back together, they would make a firm connection, but they did not. When I took the watch apart again to investigate, the connector was clearly not attached. I reattached it firmly, reassembled the watch, and powered it back on. The watch stays on now, so I'm pretty sure that was the issue.
This step is really difficult, and I'm still not sure it was necessary. The core assembly is really packed in there, and it took me several attempts, lifting from various corners. Don't pull by the circuit board. It will bend if you're not careful. You've got to get under the core assembly. I had the most luck starting next to the display connector at the top, then moving to the sensor on the other end of the board (barometric sensor), then moving to the speakers on the left, and finally lifting from multiple points once it was out far enough. In really hoping I didn't damage anything.