Got it - "So, the controller's cable loops back into itself and plugs into the Pi. The Pi takes in power and outputs over HDMI." threw me - "loops back on itself" - so this could be cleaned up quite a bit on that cable with a bit of effort.
FYI, you may have seen something like this already - this is a crappy video, but basically this. The controller itself is just plastic and can be "dyed" easily using "vinyl dye" available in rattle can in any auto parts store. I prefer the SEM brand, but duplicolor seems more available. Basically pull it down to bare plastic, clean everything with alcohol, let dry, then do very light passes. This is not paint, but actually seeps into the plastic, so it's permanent. with stencils/whatever, you can do cammo, retro 8 bit graphics, whatever.