I had a preprogrammed NodeMCU (ESP8266) chip laying around with a FastLED library and test patterns already there.
At this point, connecting Pin 2 to the Data Input of my PCB and connecting power pins should work unless I fry something.
Here's what happened after I connected everything together:
And then I was able to take a video of the display in its full glory, still running test patterns:
It works in a beautiful way that is hard to describe or convey even with video, I think you have to see it in person to get the full effect.
Next steps: optimizing the 3D model and PCB, making this modular and making 2 or 3 different sizes of the display!