Well, to close this out, the solution was connecting the DC ground to the mains ground. Thanks for the tip about measuring the voltages, I checked between the +12v DC to mains ground; the ATX supply read 12v, while the dedicated read as an open circuit. I'll update if anything goes wrong. Like a fire.
Sadly, I think I broke the USB-power mode on my RUMBA board in the process of trying to get this working, but luckily, that's not something I need most of the time. What (and if) I actually broke isn't something I'm capable of diagnosing (my guess is a diode?), but if someone wants to try... it's clearly not directly related to my original issue. But I'd appreciate it. Maybe. If I every find out I need that functionality.
Sadly, I think I broke the USB-power mode on my RUMBA board in the process of trying to get this working, but luckily, that's not something I need most of the time. What (and if) I actually broke isn't something I'm capable of diagnosing (my guess is a diode?), but if someone wants to try... it's clearly not directly related to my original issue. But I'd appreciate it. Maybe. If I every find out I need that functionality.