Is the SSD recognized in the BIOS?
Yes, the SSD is recognized in the BIOS. I can even view and modify files (I backed up the more important ones) on another computer. The repair just wouldn't find the Windows Installation.
I did just end up reinstalling my OS. Faster and easier in the end, it seems. We could still try to figure out the problem in case someone in the future has the same issue as I did. I just never seen anything this bizarre before.