It looks like 4 D-cells will last about a month before the voltage dips to the point that the vibration motor turns more slowly and takes longer to dispense a nut. The cheap store-brand batteries I'm using hold about 10K mAh.

I looked into rechargable options for alkalines, like fast-charging USB power banks with 10K+ mAh. However the dispenser works best at 5.5+ volts.

So, I think a voltage doubler ot boost converter will help me here. The motor works with 9V as well, so if I control the current I can probably hit it with 10-12V for short periods. This would let me get more out of the D-cells and open up some possibilities for powering the thing with a 5V rechargeable source that is not too expensive.

I'm already using a power bank to run the camera. 10K mAh last about 20h.

I'd also like to make the Pi only enable the camera when the PIR sensor is triggered - this would greatly extend the life of the camera on a powerbank.

In the end, this things should be able to be left unattended for at least a week with everything working.