After finishing the latest experiment with LED lighting powered with batteries, I've come to the conclusion it just isn't possible to meet my requirements of back lighting the epoxy sections and have enough battery power to last a reasonable amount of time. With these two setups, 2 1.5v AA batteries powering a 10mm 3v 100ma LED and a 9v lithium battery powering 3 3v 20ma superflux LEDs, I was only able to power the lights for 48 hours. In addition, I would need at least 2 more 10mm LEDs or 3 more of the superflux ones.
So it looks like the only way to really back light the sculptures is to plug it in. Although I still don't like the idea of having to plug the sculpture in, Paula McCullough suggested that I make the sculptures stand alone pieces (like a standing lamp) so that the power cord comes out of the bottom and isn't so much a distraction. I think this a good idea, I just don't like the idea of having to design this extra element to the sculpture - not sure how I can do something that will look good and still be priced at a level that I can get paid for my level of effort. I'll put it aside and think about it for a while.