I finally settled on a layout that uses 14 LEDs, two 8-bit shift registers and an ATtiny85V(though even a lowly ATtiny25 would probably work if I simplified the code, I wasn't sure how much program space I'd need and the cost difference is negligible). I've used a socket for the microcontroller so I could test different patterns and animation speeds. After running for 50 straight hours(with a somewhat above average "load" animation), my generic AA alkalines(fresh when the test started) were measured at 1.71 volts. It was still working, albeit with very low light coming from the LEDs.
So here is my first Instructable, for your enjoyment and/or education. See a video of it in action here(it doesn't actually "fade"; that's just my camera being slow) and showing off newer patterns here(sorry for the color balance). Hopefully my girlfriend likes it, and I hope you do, too! Please let me know if anything is too confusing or if you have any questions. If you decide to make one yourself, or if you're inspired to build something similar, I'd enjoy seeing your results!