We need to progress past triple A's I think, and establish a slightly better, at least bigger capacity battery. I've used 18650s for a lot of things, and they function decently well for most things. Aren't as common as your double A's, and triple A's though. However, they aren't some specialised hardware, and can be picked up relatively cheaply, and easily from a variety of places.
18650 is definitely a good idea; Li-Ion and common to find anywhere. Only downside is the cylindrical and large shape. But I guess it may be possible to accommodate for it in a device with Q1's (or Passport's) thickness, especially since you only need one. However, it may be overkill in capacity compared to a Nokia BL-5C, which is also slimmer and lighter.
Yes, 18650 is a thick boy, Li-Po pouch would make more sense, but one that's standardized within the industry with like a three-pin connector.