I ran a 285/70/17 on my 2.25" leveled NNBS. It was a tight fit, but no rubbing. The new bumper will fix your clearance issues on the front side, but I don't think a 35" will clear the back of the front fender without some major cutting. I'm thinking the largest you can fit would be a 295/70/17, yes, they do make one!
http://www.gmfullsize.com/forum/showthread.php?t=109335
Looks like some are running 35's with just a leveling kit! I was wrong![]()