Actually, I think I fixed it. Turns out it was a driver problem, probably. Everything else on the PC was working fine; it was only when it went into sleep mode that it started doing it.
What I discovered was that my Asus updater was telling me that the BIOS I had was the current one, when in fact it was not. Asus website had a newer version of the BIOS. I downloaded it, updated it, and lo and behold, the BSOD stopped when I put the computer into sleep mode.