For getting the lights to the outside of the case you should check into fiber optic cable... well actually you would probably only need a few strands for each light.
I would check around places that repair medical devices as many fiber optic cables are used in surgery and when too many fibers break they either repair or replace the cables, so you might be able to get some broken ones for free and be able to get some usable lengths of fiber out of them/
Fiber is easy to use as well, simply put several strands together, wrap in dark tape and put one end almost touching the light source, and at the other end secure the strands to a lens (small disc of plexi/plastic/glass).
Good luck