So I put my system in Clean Boot and waited for about an hour and the BSOD appeared. After the BSOD appeared, I reset my computer to start normally.
I'm not sure if this is of any importance, but the BSOD always appears around the 28/29 minute mark of the hour. It doesn't matter if I just turned the computer on, or if it's already on and being used; the BSOD always appears at that time with no fail (except in safe mode). I mentioned this in the original post, but I wasn't sure if it was significant.
I have been able to prevent the BSOD from happening by setting the computer clock back 20 minutes, waiting for the 28 minute mark to pass by in actual time (using my phone's clock to check the time), and then setting the computer clock back to the correct time.
I have used this method multiple times now and it always works; the BSOD doesn't appear. I'm not sure if this information will help, but I just thought that I should probably tell someone anyways.