First thing to consider is bike fit. No amount of posture correction can substitute for fit.
Second thing to consider is posture. No amount of bike fit can substitute for good posture.
Catch 22, eh? No, really, check the fit first. Then be very aware of how you sit on the bike. Chest should be pointing ahead, not down at the top tube of the bike. Elbows should be relaxed, not locked straight. Grip on the bars should be light and fairly soft, not a death grip with lots of weight behind it.
Talk to the PT who is working with you on the impingement and frozen shoulder. Have him/her assess your bike fit as it relates to your body. Most insurances cover fit assessment if it applies to a physical issue. The PT will give you some posture and core exercises and be able to help you with specific issues on the bike.
Remember, you only need about 90-100 degrees of glenohumeral flexion to ride, and riding in good posture strengthens the muscles that prevent impingement! Biking is good for what ails ya'!
"If Americans want to live the American Dream, they should go to Denmark." - Richard Wilkinson