Sorry to respond again - I just figured out a really weird workaround that makes me think this is indeed a bug. If you scroll to the bottom of this documentation there is a section regarding "Allow labels to overlap border (Maplex Label Engine only)." If you go to the map property dialog box, this option is checked off - so what Greg and I are describing shouldn't be happening. The thing that made this map property "stick" for me was checking it (to do the opposite of what I wanted), hitting ok, and then going back into the property dialog box and then un-checking it again (as it originally was). Only then did my labels not overlap the border. I haven't done an exhaustive check to make sure this works all the time, but I think it does....
On top of this probably being a bug, I understand that this is a "global" property, but it seems like it would make more sense for this property to be set in the label class pane instead of the map properties. It took lots of creative Googling to find the documentation referenced above. Thanks!