I had a patient with a brachial plexus injury that happened when she fell backwards and grabbed onto something infront of her - pulling the arm and stretching the plexus. She was in agony to be honest and from my (allbeit limited) experience of dealing with them, recovery can take a long time and its important the patient knows that. Like you, i taped the shoulder into elevation to offer some relief but it only lasted a while before that position became painful too. Recovery was spontaneous but I left that place of work and don't know how she got on after the first few sessions.
I did an inservice presentation on them, its a powerpoint and might give you a few ideas but from my reading for it the jist of the principles of management were education and psychosocial support (as its a nasty long term injury), ROM exercises to prevent secondary injuries and pain management. For that you could try things like TENS, massage (might be an idea to start distally as massaging the shoulder could be pretty painful - whatever works best i guess), hydrotherapy and trigger pointing. Happy to send presentation to you if you PM me an email.