Kudos to the original from jgillick (https://www.thingiverse.com/thing:615934) and Blackbird7171 for his remix and to RaMcHip for his remix that reduced the plastic and added lids (https://www.thingiverse.com/thing:469115). I just added labels to the front of the base dispenser. Have printed the AA and the tolerances are absolutely perfect.
AA dispenser with extension holds 18 batteries with lid on. With an extra extension it holds upwards of 24/25.
Print as many extensions as you need to fit more batteries!
Deepened the labels and provided a wedge beneath the "A" overhangs so they print better. Also added all individual models and battery size plates (AA/AAA).
While printing another copy of the AA plate, I noticed the labels were a little too deep and the back wall wasn't printing as cleanly as it should. I've replaced all models that have labels so they're not quite as deep which solved the issue.