I had thought of mounting tiny LEDs to laminated plastic strips that could be glued to the frame. They would have the wires routed inside and maybe could be covered in some type of plastic gel?
Joe, I still like the idea of laying out a PCB to hold the LED's, it would make the wiring much simpler. If needed, you could add buffering for driving the LED array. I'd run the LED board down the side and make the wiring connection to the back of the PCB. Here's a simple test I did some time back for an LED array, but this one only had three sets of LED's, but you get the idea. For your application, I'd make the board skinnier and run the LED's in line, the board could be vary narrow.
I was just doodling one day thinking about a light chase board and started this. The extra connections were because I was going to have five sets of three LED's, just never got around to playing with this again. The connector holes on the right could be just pads on the back side to solder the connection leads to. You could even incorporate balancing resistors if needed.
As far as the circuit power, like I said, you could easily run the LED's on a fraction of the power that stuff like headlights run on, so I doubt buffering would be needed. Also, there aren't 40 pairs of wires when you put them all on a PCB, for twenty LED's in groups of four you'd have six wires, five switched and one common.