I think I've solved the issue. Posting here in case anyone else sees the same thing.
First background:
I have found that in the drawing I am editing, there are MANY Blocks with duplicate attributes. Not sure why, this drawing was previously done by someone no longer with the company. However, on ALL the other ones, I was able to go into BATTMAN and delete the duplicate without issue. Only the original Block I first edited continued to have this issue. I believe the difference, and a possible way to duplicate my issue (Note: I'm using AutoCAD 2018) is that in that original block, I mistakenly (?) deleted the "Attribute Definition" object in the Block editor BEFORE I tried using BATTMAN. That seems to have resulted in it continuing to appear in the "Enhanced Attribute Editor" but not appearing in BATTMAN.
That being said, the issue seems to have resolved itself. When I saved the drawing, closed, and re-opened, the offending attribute no longer appeared in either BATTMAN or the "Enhanced Attribute Editor". So I guess it's just a memory glitch of some sort.
Anyway, to anyone else reading this: I would recommend using BATTMAN first before deleting duplicates in the Block Editor. If you've already deleted it in the block editor, and it's too many actions afterwards to reasonably undo, then save, close, and reopen appears to solve it.