Instead of putting in batteries one-by-one, with this you can dump them in and take one as needed. Should also help you take the oldest battery first.  It should let you hold AA, C, and AAA batteries (AAAs are shorter so they may rattle around a bit). It is 2 x 4 gridfinity squares in dimension.

Updated base of hopper to make it easier to remove batteries.

My other gridfinity designs.

Also check out this nice AAA insert by by @neclimdul.

Based off of Zach Freedman's gridfinity system.