I can only talk of my experience when I felt mine go during a set of floor presses. It was a nagging pain right on the AC joint itself and put an end to all pressing activity.
I tried ART and I believe it helped, although it seemed to return after therapy sessions. In the end resting it as much as possible and training around it worked - but it took the best part of 10 months to get to that position.
I would encourage trying some sort of myofascial release, such as ART, particularly on the posterior shoulder capsule, as this does help to return the shoulder to its natural position and allow healing, before opting for any surgery.
I believe my shoulder problem may have been triggered by tightness in that area, and it did respond well to the ART, although realistically it took an additional rest period of around 4 months following ART until it was healed enough to start seriously loading the shoulder again.