Ok, so I unscrewed it, but here’s the moment of glory!
4 screws on the bottom (Not under the rubber feet; in their own holes. Wow, this thing really WAS made for hacking) and it just pops open.
The power switch and LED just slide out of the bottom shell as one unit, the A/V cord pulls out too, and the only things left holding the bottom are the power wires. A quick zip with the desoldering iron fixed that problem.