Estimating Battery Life
First, you need to make a realistic ballpark estimate before going to intergraion of discharge curves and buck boost converter inefficiencies. 

The estimate would be: at 3 V input supply and 1.11 mW, the device will take about 0.45mA average (assuming 80% efficiency of converter, if any). The Duracell discharge curve says about 650 service hours at 5 mA discharge rate. At 0.45 mA it will take about 11 times longer, or about 7200 hours. This is about 300 days of operation. Which is about 20% short of one year. 

Conclusion: you can't guarantee this device to work for a year from 2xAA batteries. No amount of more accurate mathematical massaging of discharge curves would change this conclusion.