BIOS recognizes SSD but Windows 10 installer doesn't

[jrd1234]

I'm on day four of trying to solve the most maddening issue. (This is also my fourth time trying to post this; I apologize if there are multiple posts, but I can't figure out why it won't appear. I included pictures in my previous posts, but not here, since I'm guessing it might be due to some kind of automatic moderation.)

My HP 17-by1053dx notebook was previously running Windows 10 (64-bit) just fine. During the installation of a recent Windows update, however, it stalled. When I restarted the machine, it failed to boot, returning a "Boot Device Not Found" error.

After poking around, I discovered that BIOS can detect my SSD, but that the Windows 10 installer can't.

Here's the really perplexing thing: Different versions of the HP Hardware Diagnostic UEFI disagree about whether there's an SSD installed! One finds the SSD, and in that one it passes all of the diagnostic tests (SMART Check, SHORT DST Check, Optimized DST Check, Long DST Check). The other returns a "No hard drive installed" error.

The BIOS Boot Manager can also find the SSD.

If possible, I'd like to recover the data on the SSD, but I'd happily settle for a clean new installation of Windows 10.

Things I've tried:
- Updating BIOS to the latest version. It was F. 47 before; it's now F. 56. Since the change, booting has resulted in a BSOD with an "UNMOUNTABLE BOOT VOLUME" error.
- Enabling and disabling both Legacy Support and Secure Boot in BIOS, trying all four possible combinations.
- Running the startup repair program available through a Windows 10 installation thumbdrive. All of the similar troubleshooting options there return generic errors.
- Troubleshooting through the command line available through a Windows 10 installation thumbdrive. Specifically, none of the following does anything useful:
chkdsk /r c:
bootrec /fixmbr
bootrec /fixboot
bootrec /rebuildbcd
sfc /scannow
diskpart (followed by "list disk," which doesn't show the SSD)
All return errors of the "no hard drive found" variety.
- Reinstalling Window using a Windows 10 installation thumbdrive. The installer is unable to find any drives on which to install it.
- Copying the Intel Rapid Storage Technology driver available in f6flpy-x64.zip to a different thumbdrive, then attempting to load it in the Windows installer by clicking "Load driver." This installs the driver, but Windows is still unable to locate any hard drives. I tried the most recent driver, as well as two older ones.
- Reseating the SSD.

Any help would be greatly appreciated!