If there is no painful arc and you don't have symptoms until at the very end of elevation, you probably want to look into stabilizing your AC joint. That is the main time this will produce pain and make noises. Popping can come from multiple sources such as tendons sliding against bones, a tight posterior capsule or pec minor allowing the humeral head to lip on the anterior labrum or against the coracoid process causing anterior impingement , AC joint during elevation, and there is a phenomenon that I have called snapping scapula. If you can physically stop the problem, which is what I do n the clinic, then you he your answer. Try some strong tape over your AC joint and repeat" the "offending" movement to see if there is any change and if so does it remain so repetitively.
Try mid-range push ups or push up position only on your arm. Rule it out or in 1 a time. There are very good sensitive and specific tests and a lot that have no evidence to support them. I can give you an excellent reference if ever interested