TL;DR: I got through all the steps in my previous post, and now have a semi-functional Windows install.
After getting all the data off my desktop PC SSD, I re-mounted it in the PC, using a different SATA cable, and tried some stuff. The drive was still not bootable, and attempts to repair it were still completely unsuccessful. I did manage to boot from a recovery USB drive that I created via the Dell site. None of the repair options that I could run from that worked, but doing a fresh install of Windows 10 does seem to have worked. At least, it’s working so far.
I’m copying some files back to it right now, while also letting it download Windows updates. That’ll keep it busy for an hour or two. Then, I’ll see if I can reboot and install the updates. If that works, then I’ll look into copying more files back and installing some software. Getting it back to where it was will probably take all week, assuming it holds together and doesn’t start blue-screening again.
If it does keep working, then I have to say that I’m not at all sure what was wrong in the first place. It almost has to have been a software problem. It wasn’t the SATA cable, or the port. If it was either of those, I would have had more luck with it prior to the nuke & pave reinstall. There’s probably no point in speculating too much at this point. I’m just going to keep pushing forward with it, and see how far I get.