Just a couple thoughts...every increase in tire diameter will rob more power. It takes more torque to turn a larger diameter tire and even more additional torque in a soft material like sand. That also means more fuel consumption. If that's not a concern, don't worry about it. If it is a concern, I'd try to go wider but not taller, or maybe only one size taller.
There are also some specialized tires by Dick Cepek and/or Mickey Thompson that come in 13" or 14" widths at only 31" diameter or so. They would probably require wider rims, though.
Some tire manufacturers make a 31 x 11.50 in 15". That isn't a widely popular size, but I have owned some tires of that size before as replacements for 31 x 10.50 on a Bronco and a Ramcharger (Bridgestone Duelers). It's not a big difference in width (1"), but there is more rubber there to float out wider without increasing diameter.
To go up one size in diameter, those rims will no doubt fit 32 x 11.50 tires, and that is a fairly common size. I've done them on a Ramcharger before, also (General Grabber AP). I think you'd probably get the next size up - 33 x 12.50 - on those same rims, also, but that's probably the biggest. I can't speak for a Suburban specifically, but for the Ramchargers, even 33 x 12.50 will fit. The rears should be fine, and I don't think the fronts rub, at least not on the Ramchargers. Some of our state DNR's Ramchargers and military-surplus Chevy Blazers had that setup with Goodyear Wranglers in 33 x 12.50 15".
I just got a new set of tires for my '99 Grand Cherokee, and I got just about the largest size that would fit without rubbing...255/70/16. I wasn't sure about them at first, so I had the tire guys mount one and test it on the lift first to make sure it fit ok. The lift was the kind that didn't let the wheels "dangle" down as low as they go...it reflected the normal position of the wheels. They turned the wheel all the way left and right, and the clearance was fine. So, I'd just have your tire shop do that...a bit of trial and error to see what fits the way you want.
My $.02. Good luck.