I saw a 2500hd gasser yesterday with 315 75 16s on the factory wheels.

I really liked the look.

Does anyone run this combo and if so, what kind of trimming did you have to do?

I had to trim the wheel well side of the bumper ( I know i should not have to say it like that, but there are those......) a couple of times. Did the initial trim at the place I had the tires and lift installed, then found that while turning while backing into my driveway, it rubbed, more trimming. Then pulling into a parking spot with a little more speed than really needed, rubbed some more, and had to trim some more. I have since taken the time and jacked up the front, one side at a time while turning to ensure I have a good amount of clearance. No issues since. I do have to replace the black plastic fender well liner because is ripped after catching during a turn. Lesson learned there. Good luck.

My first guess would be a lot. Plus with a tire that wide on a 6.5" rim you're going to wear out the centers fast. Let me know how it works, i bet it would look really good.