I would agree with Physio Dude. especially in relation to the chin ups and end range stretches. Your physio should work with the surgeons advice. Stability of the gleno humeral joint and the scapulothoracic should be the highest priority and this can be done most safely in unloaded positions such as prone with the arm dangling over the side of the bench. I you are up to free weights then you must be able to lower the weights down ( eccentric movements) without the muscles shaking and the movements should be smooth and controlled. The exercises on the ball sound great to me though as this encourages good muscle cocontractions around the G/H joint

As far as running is concerned I wouldnt be as concerned about gently running to restore general as dangling on your arm Its a lot to ask of a repaired labrum!

The last thing that you would want is a long standing shoulder problem so I would think that you should take rehab one step at a time and only progress when you have achieved really good strength

good luck