I've cut out the board and made a note of where the wires came from.  There were 4x 26650 lithium cells.  As I can't tab or solder them myself and I don't think the holders I've found will work well, I'm looking into potentially just breaking apart a ready-made battery and stealing the cells.  It looks like it will be cheaper.  However, I don't actually know how the intelligent circuitry works.

So before I move on anything, does anyone have thoughts on replacing 4x 26650 batteries with 8 different cells?

(http://www.amazon.com/gp/product/B00OCLBL60/)

The 4-cell batteries I've found all are rated too low, and they aren't comparatively very cheap either.  A 4-cell roughly 2000mAh battery runs roughly $25.  An 8-cell rated at more than twice that is a little less expensive.  If I recall properly Apple's was rated either at 3300mAh or 3800mAh.