I really want this PP3 battery you have at 550mA!!!

Are you sure you have the correct mA/h figures?

Usually these are in the range 150 to 170mAh.

What requirements has your circuit? (I flow, time to operate before die etc).

I would surely use AA, maybe 3 of them for about 4,5 Volts or 2 of them with a boost regulator.

Ioannis