Other than shooting an arrow that is a little heavier than needed, is there really a big downside to shooting an overspined arrow
Heavier than needed? It might be heavier, but that is a good thing when for most hunters.
I personally disagree with trying to get an exact spine match with most carbons. So many have such a wide variation in actual measured spine in a dozen, that you end up shooting some that are on the weak side, and some that are stiff. I think most are much better off shooting all arrows on the stiff side. Your ACCs are probably an exception to this.
I find that I get great broadhead flight when tuning my setup with all arrows on the stiff side.