Love this project, hate wasting filament on support. Had a possible interesting idea:
You currently have a rectangular cross-section (and yes and I know a square IS a rectangle). Lose the top crosswork portion, then close in the sides to form an equilateral triangle cross-section and print it on its side (can't print with the LED channel down because of the curve required for the ellipse. Gently sloping does NOT require support material so less waste with the same aesthetics - maybe even a bit more "artsy"!!! Add the "snap together" capability and it is ready for prime-time!! I think the triangle form would also be stronger as well. The base pieces could use a slight tweak on the ridge around the middle- if you slope up to below it, rather than making it a square and then add some triangles inside that slope up the lid, then it could be printed upright.
I am for keeping the ellipse but I would make it so that lower side pieces (and base) are printed twice with a single "keystone" to connect the two sides. Heck in the model just duplicate the piece in the STL so when you print it prints two.
Just a thought...