Step 1: Disassemble UPS (not shown). That includes unplugging it and removing the battery, and taking the outer shell off. This was a dumpster rescue that was missing the battery entirely. Be careful. Lots of capacitors and transformers inside. See the disclaimer in the title. Not highly recommended.
Step 2: Drill a hole in the case, near where the battery wiring harness enters the battery chamber. I used a 1/2" drill bit for this.
Step 3: Make a grommet. I used some silicone air hose for my aquarium, cut a length of it, then split it. I used a few separate pieces.
Step 4: Re-assemble, Hook up a much bigger battery than what's supposed to be inside.
I accept no blame for any of the many things that could possibly go wrong with this.