I had decided to go with 12 volts running sets of 3 LEDs with 68 ohm resistors, but then I found an old transmitter battery and an old receiver battery lying around in my basement. I thought it would be a lot easier to put them together without splitting the receiver pack in half, so I ended up making a 12 cell battery. I also dug through a little drawer full of loose resistors that I happen to have, and I found a handful of 33 ohm and a handful of 39 ohm. These will run sets of four LEDs in series, as confirmed by a test that I did last night.
The great thing about using my mismatched bulk supply of resistors is that when the battery is running down, half of the LEDs will go out before the other half. As I recall, this was also the case on my friend's airplane that inspired me to do this project. He said that this was very useful because he never had his lights go out unexpectedly while flying.