Battery Box 8881 not providing enough power
In case anyone else has this issue - cleaning corrosion off of the connections solved the problem!
To clean the contacts, I used white vinegar applied with a cotton-swab/cue-tip. I dried it off with a dry one, left it for about half an hour, and after that it worked perfectly. I watched this video to be sure there wasn't anything I needed to do that I was missing.