Oh my God...
...it was the swap trick of all things. Only swapping once might have not been getting all of the data on my CDs, causing them to have strange glitches while playing them.
I'm really happy, but I'm also kinda mad; I already ordered a 25pk of Verbatim CDs and a replacement laser. Well, I can use the Verbatim CDs to burn off more great Saturn games, and keep the laser somewhere safe in case the one in there dies.
Thank you to everyone who helped me!