I worked up a quick and simple rotary encoder tester board. It may be that a good UI for the lamp is a couple of rotary encoders. Here's a quick board that is millable on the Othermill and mounts 3 standard PCB-mount rotary encoders, an Arduino Pro MIcro, and has two different LED strip outputs.
Time to start milling, then back to materials tests.
Also, I'm putting everything that is code & schematics in this repo: https://github.com/todbot/ILOVELAMP
I'm still not sure how to properly share Fusion360 models (The Autodesk A360 is much better than either Hackaday.io or Github, but it's really closed off), but I'll try to put models in the github repo too.