They may fit if you put a leveling kit and a 1.5" body lift on. Don't know how high you'd want to go or what you want to pay but that's the cheapest route. I've got 285s with a leveling kit and rear leafs from a 2500 and i rub just a little at full lock.
Are you putting them on stock or aftermarket wheels? The more negative offset the wheel(more it sticks out of the fender) the more chance of rubbing. Id suggest a leveling kit or atleast some turns up on the torsion keys though. Some trimming of lower corner of bumper probably needed as well.
I had 285/75/16 on my stock height 04 silverado and although they were close they never rubbed . The 305/70/16 has the same diamter at 32.8 inches so you will probably be fine, the extra 20mm in width may rub in turns though.
What wheels would these be going on? I think a stock 16" rim is only 7" wide. That's definitely too narrow for a 305.
IIRC, a 9" wide rim is the minimum recommended for 305s.
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