I don't think the arm is sloppy on the spindle. Seems more like the spindle is a little loose in the bearings. When the crank arm is off, I don't have enough leverage to make it wiggle. The bolt interface on the spindle looks fine, as does the bolt itself and the crank arm.

I guess it's just time for a new BB. Maybe time to upgrade the crankset while I'm at it. I was going to spend upgrade money on a new wheelset first, but maybe I'll do the drivetrain instead.