I've also got a wager coming up - many of the envisioned uses for the project will use non-rechargeable LiIon, as existing GSM types do - and these commonly transmit once a week only, with an expected five year battery life. The batteries are 19Ah, and usually used with at least two in parallel, with a 'best' capacitor across them - the batteries have high internal resistance, so can't supply the high current pulses the modems require. So the next test will be to power it from one of these batteries (adding a best cap - I've got a space for it on the PCB) and see how long that lasts. My boss reckons that it will last more than 60 days, I reckon it won't make 60 days - so we've got a bet on it, with the loser buying lunch!
As the 18650's haven't run out yet, it's a bit difficult to predict - the 18650's are 2.2Ah each (so 8.8Ah), but are second hand batteries - so that makes it even more difficult. I'm guessing they won't make three weeks - if that proves the case, and they are truly 8.8Ah, then the 19Ah shouldn't make 60 days!.
Anyway, enough rambling on, hope this gives you some ideas.