Firstly, as you said, if the surgeon says wait a certain amount of time before you do something he has a reason for it. He saw the damage inside and knows his work in trying to mend it!
Shoulder stability will depend on the correct rehabilitation of your Wikipedia reference-linkrotator cuff muscles. A HAGL lesion may have included your subscapularis muscle tendon, check out on that. Rehab usually should include your "scapula setting" and scapula function as well. It's not just a question of how many repetitions IR ER muscles but the quality of activity in the rotator cuff to provide and maintain enough "zentrierung" of the joint throughout range etc.. Look for a physio either with excellent "Kinetic Control" experience in muscle imbalance rehab or, although I don't do it myself, "Sohier Konzept" trained physios will look for "zentrierung" and so on. You need, at the beginning, a tailor made assessment of YOUR current shoulder function and hands on individual correction. Aim for excellence. You will need your shoulder for a few years yet. Good luck