Doublechecked the minidump folder (for me, C:\Windows\Minidump) - it's empty. To be sure, I let the computer BSOD again and it remained empty. Ran the diagnostic tool, had it check only minidump files, and the folder it created was empty as well. I'm not seeing any errors that would suggest lack of read or write permissions - I can view it fine, create random folders in it, etc. It's just empty.
Ran the chkdsk using the GUI instructions of the link you sent - took about 10 min, didn't find anything, crashed as soon as computer booted to desktop. After restarting "windows.exe" stopped working for a while until it rebooted again. Haha. Haven't seen THAT one before. None of that generated anything in the minidump folder, it's still empty, and reliability monitor only recorded one unexpected shutdown in that timeframe with no further info.
Running the chkdsk again via command line interface finally got somewhere - it froze at 10%, flashed an error message, and crashed the computer. After a few repetitions I managed to see that it had apparently caught on a folder that didn't exist or something, the message doesn't stay up for long and happens only after ~10-15 minutes of sitting at 10% so it's hard to see it exactly when it happens.
Sorry for the lack of specifics - I realize that may not be very helpful.
If the info helps at all, I've run chkdsks and sfc scannow before to deal with potential issues, and reinstalled windows normally as well as formatting the drive and reinstalling windows fresh before.