If the Arduino requires 34mA in sleep, it is not usable on this project.
My favorite small PIC microcontroller 12F1840, running at 5V, uses 600μA at 4MHz, 3.4mA at 32MHz and as little as 6μA in sleep mode. Of course I would run it at 3.3V off the LiIon battery, at which it draws even less. It...