Hello,
What's the curvature of your spine from a lateral point of view like? If you have exagerated kyphosis of your thoracic spine your going to get a bad setting position of the scapula no matter how hard you try to correct it. This is going to affect the bio mechanics of the scapula in a big way, meaning you utilise other muscles to perform motions like upwards rotation of your scapula instead due to the line of pull.
Is it only on one side? If so, you might have to address things like the pelvis as any rotation in the spine will again offset the positioning of the scapula and develop different length tension relationships which will again impede function. If there's any shear force in the joint during loading you might find that your SITS muscles may over compensate to correct this thus making them tight due to overuse and therefore during any flexion of your GH joint it will cause the shoulderblade to lift, i.e. wing.
You need to have your whole body assessed in order to find out if your shoulder is the root of the problem or just a symptom. If it's just a symptom your just going to get milked by poorly trained health professionals. Spend some money and find a practitioner who is aware of the big picture.