Thanks for your assistance and, truly, time is not of the essence here. I am happy to report that I have eliminated (or at least seem to have eliminated, so far) the BSOD, but I'm not entirely certain why.
My UEFI/BIOS version F42 is what HP shows as current, but I reflashed anyway. Based on some of what was in your "old driver" list I removed the following, some of which were unrelated at all to the list:
Sentinel System Driver Installer 7.5.0 (which I have no idea how it ever got installed in the first place)
CoreTemp 1.0 RC6
CyoHash (highly unlikely to be the problem)
JAWS 17 & all Shared Components (a possible culprit)
AOMEI Backupper Standard (driver file in the list)
& MiniTool Partition Wizard Free
Now when I'm performing the same activities that were either instantly giving me the BSOD (trying to download from a device) or triggering one at some point when working with FastStone Image Viewer they're not happening.
I wish I had had the patience to do one-by-one removal so that I could have determined when, precisely, the thing removed resulted in the BSODs stopping, as I like that kind of pinpointing, but I didn't.
If it's possible, and really whenever you have time, to figure out what was in that original driver list that might not be there anymore I would be happy to generate whatever report(s) would be necessary to determine that. This has got to be traceable to one or some small set of drivers.
Brian AKA Bri the Tech Guy (website in my user profile) - Windows 10 Home, 64-Bit, Version 1803, Build 17134
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