Got to talking to a guy on IRC who mentioned he had the exact same problem a while back. He couldn't remember how he resolved the issue, but he found that burning the ISOs to CD-Rs worked as a temporary fix. Not having any CD-Rs on hand, I dug through some boxes and got my Saturn collection out. Lo and behold, my computer can run CD audio directly off a CD without any issue. It's gonna be a pain in the ass having to burn games I don't own, but at least I have a workaround now.
To everyone who tried to help me out with this, thank you!