The power circuitry on-die is quite impressive.  It should work with any 3.7V LiIon battery.  Sparkfun sells an impedance-matched 6 Ah battery pack I've been wanting to try out.  You'll at least want protection circuitry on any battery you try out though, to protect against fire in the case of overvoltage/undervoltage and shorts.  Most batteries have this, unless they're really super cheap.

You need to have something connected to the thermistor terminal, but in reality it could be something as silly as a 10k? resistor.  If you stick a resistor on that's too low, it will think the device is on fire.  Too high, and it won't recognize there's a battery attached.  If you're going to do live insertions and removals of the battery, I think you'll make sure that the thermistor gets mechanically connected last.  Otherwise, again, it might think it's on fire and shut down.

A larger battery would just take longer to charge.  There's a timeout of I believe 20 hours, so you should be good.  The onboard charger should be able to handle it.  But again, make sure you use a cell with protection circuitry!

During development, I actually had a 2700 mAh laptop cell that had leads attached.  That was a nice battery.

Thanks Lurker, I may just have to look at the sparkfun battery. If anyone does have an NP-120 battery handy, it would be a great help if they could probe for the normal resistance of the thermistor at room temp. Then I could either find a similar thermistor or just tack on a resistor as you said.

Thanks. I found a slightly larger Li-ion pack at 6600 mAh that is better suited for external use. While we are here, does anyone know what connector is used that connects the battery holder to the main board? The three-pin one? I will have to buy a replacement.