I don't know if you're driving an NBS or a Classic, but FWIW I saw an 03 Avalanche with 285/70R17s (Goodyear Wranglers) and they just barely cleared. I was considering putting the 285s on my 05 Sierra but realized they'd protrude past the body a bit, and I don't have fender flares. Tires protruding beyond the body is illegal here and I didn't want to add flares to make it compliant, so when time comes for new rubber I'll be getting the same size I've got, 265/70R17s. They're pretty beefy already.
As for fitting the wheel, the BFG AT/KOs are listed as fitting a 7.5-9" rim so depending on the tire you can probably squeeze them on there.