It is obviously an interesting proposition to switch serving handedness, but as you pointed out it really won't allow you to progress as much. I would certainly be worried about the time it takes to swap back to being right handed especially when the return is being played quite fast on you.
Of course if you practised hard enough, you could take such a lefty serve into a real weapon at least some day. However, typically since you would only be using your left hand to serve, I don't think the progression to make it viable is worth it.
Have you tried various techniques to help ease the pain on your right shoulder? As in take adequate time away from the game, get plenty of rest and do drills and weight lifting reps for your shoulder. Regardless, I'm sure you have talked to a doctor about your shoulder, so what options did he give you?
Got an MRI 18 months ago.
Surgeon says try physical therapy first, because surgery is expensive ($12k out of my pocket) and painful (1 year until you return to tennis).
So I stopped tennis and did the therapy.
I can do everything at work and home that I need to with my right arm.
And I can play tennis.
But I can't serve with my right arm.
So serving with my left makes tennis possible.
And yes, people do lob me. I can hit 5-10 overheads a match right handed without pain.