I think the BC547 is fine, I was just trying to account for all the current consumed in the circuit, since it adds another 1/200 = 0.5% to the current consumed by the EEPROM on the NPN base. It will also consume power in the form of a voltage drop, Vce in the saturation mode (0.25V max).
The MOSFET, on the other hand, will consume practically nothing on the gate, and will drop the voltage less across Vds. For example, with Rds(on) = 5ohm, and I = 5mA, Vds = 0.025V. This lends itself better to operating at a lower voltage.
I agree, I'd go with 3V power supply. So, in my CR2032 example, you'd connect the two cells in parallel instead of in series. Those cells will provide pretty much all their power above 2V.