Got everything back together—seems to be working
Battery wouldn't hold a charge. Front of phone was bloated (discovered OEM battery had expanded (overheating?) during removal.
The step-by-step instructions were straightforward, and the video of the lady taking apart the phone was a great example of what I needed to do.
I'm not totally sure I did the reassembly right, because the first time I got everything back together, the display had a high frequency flicker/blinking that was noticeable at the corners of the display. Like the alpha channels weren't rendering correctly. I wasn't sure if I'd damaged things, so I took the screen assembly off and reseated the LCD ribbon connectors (the 3 towards the top of the phone. The flickering was reduced upon the second reassembly, and it went away after an hour. The next day (today), the display seems fine, but I'm worried I may have damaged it. Has anyone experienced similar issues?
The tip from the video about having a place to put the screws is no joke, those things are microscopic. I used a dinner plate with raised edges. Also, I should have paid more attention to where the directions said to keep track of the 4 different screws holding the LCD ribbon cables in place. I didn't note their locations when removing them, and had to try to eyeball them to judge the sizes when reassembling everything. Really tough to judge the difference between the 1.2mm screw and the 1.3mm screw. Maybe that's what's causing my display flickering? Overall not a bad process, but make sure to prepare (make a backup of the phone in iTunes before starting), as well as mentally (we would have had to buy a new phone if this had failed). Glad it worked!