Larse, how about kettlebell military press with relatively light weight?
notice how the weight is rotated up, not forced up
http://www.youtube.com/watch?v=hIJopHx7LWc
It seems to me to combine moderate strength building with stability and none of the heavyweight stress.
I know each injury is different but in my experience moderate use is better than no use even if slightly painful ...
I did some of those presses with a weaker left shoulder due to mild pain from breaking up old injury after a ski crash. Eventually my injured left shoulder got free of pain and became as strong as the right shoulder. My original injury years earlier was caused by stress in a bad position, and was fixed by going on a motorcycle trip! In both cases more than a years rest did not solve the problem, it only reduced it a bit, but a short period of active work fixed it.