There you go. The only part is that, from what you said, there is a cavity in the front. Depending on the size of the converter, you would have to run the wire up to the front of the unit then throughout the ups to get it where you need it. Shouldn't be that bad though I would think. Also, is there any outlets on the ups that just work as a surge protector, not a battery backup? I think some of them will have a couple outlets that are straight through power and will just shut off when the power goes out. If so, you won't have to do the relays, just plug into that. BOOM, DONE! lol Nice thinking.
**Lightbulb!**
Unless you don't have one. You could just take a 12v transformer and cut the end off of it and just use the wires to power up what you need. Again, you would just have to watch the amps.
AC-DC Power Supply