I finished the electronics today. The RGB and white LEDs on both sides can now be controlled via the main controller over sACN/E1.31! I tested everything out with QLC+.
The DMX controller seems to work just fine without a ground wire. My understanding of this is that RS485 and thus DMX requires a common mode voltage between -7VDC and +12VDC, so as long as the grounds between my two power supplies (one for the main controller, the other for the lamp) don't have a voltage differential greater than that, then I'm fine. They're on the same house AC and are made by the same manufacturer, so that probably helps.