I rub to the right at full lock with those exact tires, but in 35's and +18offset rims. I have 7.5" of total lift... not quite sure why either.
I dont think you are gonna be able to squeeze those 37's w/ just a 6" lift. 8" lift would give you minor rubbing. Now maybe a 6" lift w/ a 3" body and you would be set for 37's and no rubbing.