Thanks for the help!
Unfortunately that doesn't work. It will snap to either the left or the right side of the symbol, but not the center.
Under normal operation, it will function exactly like you showed in the AVI in that post... but some parts that I have to work on don't operate like that. I have to assume that some random setting is changed with those parts in particular that is causing this behavior.
Even more odd, I have a few files where on Sheet 1, the Datum Symbol feature acts completely different than on Sheet 2 on the same file.