Ok, guys, I have finally fixed it for good (I hope).
As mentioned earlier, I snipped two sections of a Molex-to-SATA power cable and soldered them to the BACKSLASH switch and soldered the other end to unused key's pads. At first, I connected them to the unused pads next to ENTER, but the QMK Configurator did not allow me to access that spot on the PCB separately from the main ENTER. I probably could have figured out a way to set up a QMK environment and make it work, but I am dumb and lazy and would rather just use the configurator. I noticed that the configurator does allow for a split backspace, so I desoldered the wires from ENTER and connected them to the outermost BACKSPACE spot. Then I remapped BACKSPACE to BACKSLASH. On the keymap it's basically the reverse of what a split backspace layout would look like (BACKSPACE on the left and BACKSLASH on the right), which still works since I'm using a regular ANSI layout. I put some electrical tape around the wires and at the solder point since a stabilizer screw goes right on top of one of them.
Crisis averted (for now).
Thanks for all the help, everyone. This was a pain in the butt, but I wouldn't have been able to fix it without your suggestions.