Fix your shoulder before you do anything to further aggravate it.
Instead of DL, why not do box squats? You can try wide stance to get a feel for what pulling sumo would be like and use regular or narrow stance to build back up to conventional pulling. I've started using box squats a lot more and I think they really do carry over to DL nicely, especially if you have access to a safety squat bar.
You could also do paused front squats if your shoulder allows. I've also found them very helpful to my DL. Just don't go for more than triples, I generally start to black out past that point because the bar chokes me.