I daily your truck’s “younger brother”, a 99 K3500 c&c dually. Anything over an LT235/85r16 you will need rear wheel spacers. I run 235/85s up front, 265/75s out back, as both are 31.6-31.7 inches tall. To stay in that range with period correct tires, you would be looking at a Deestone 503 in 7.50-16LT, E (10), F (12), or G(14) ply ratings. Speed max goes way down as ply rating goes up.
Modern radials? 285/75r16 is 33-11, 315/75r16 is 35-12.5, you can get either in AT or MT. I like the sizes I run, but will likely switch to 14 ply RT in 235/85 all around. The K3500 is more tow pig than offroader. IF I don’t straight swap it for a friend’s ‘04 cclb duramax K3500 dually. He’d prefer a gas engine 5spd, I don’t really care either way.