What size tires can I fit on a C20?

[slotard]

I have a '73 C20 Camper Special. Stock suspension, probably staying that way for a while. Utility bed, which appears to have plenty of clearance as long as the tires don't stick out any farther.

I'd like to get a little taller effective gearing, as well as go to ATs rather than the entirely street oriented tires that I have. I don't leave pavement too often, but ATs don't compromise too much. I don't drive it a lot, so the tires will likely age out before they wear out (the current ones are getting old, but aren't cracked much yet).

I'd prefer sticking to the same size front and rear, so a spare doesn't make the truck sit crooked (and so I don't need two).

Since I don't leave pavement too often I don't flex it out too often, but I'd still prefer it not rub when I do so. Some minor trimming is fine but I'd prefer not doing too much. My current tires are 245/70-17s, so 30.5" tall. How much taller can I go?