Yes, all this helps a lot. Thanks, guys.
According to the documentation I could find, the Raspberry Pi model B requires 700 mA, but it's also got a WiFi dongle drawing power from the USB port, so let's say 1 A to be safe. I calculated my IR LED array will draw approx 500 mA, so for a safety margin let's round the whole thing up to 2 A total.
The plastic housing I'm intending to put all this in has a nice molded AA battery compartment with center tap, so I figured I'd use 14500 sized Li Ion cells to take advantage of that compartment. A lot of 14500 lithium cells are advertised as having protection PCB's integrated right into them. If this is the case, can I omit the protection IC from my design, as long as I mark it for use with protected batteries only? Or would you recommend a 2nd protection IC in the power supply/charger anyway?