I'm running 35s on my 4.10 Rubi 6 speed. I would not be happy with it running 37s. With 35s I noticed a significant loss of power. Usually have to downshift going up more than a moderate hill at highway speeds. I can't imagine how much worse it would be trying to turn even more meat.
You would also definitely have to trim your rails and pinch seam. With 35s it is somewhat optional, with 37s they would have to go.
And personally, I think 35s look pretty good under a 2dr on a 2.5" lift. 37s would be a little too much for my taste.