Hunter, didn't I read in another thread that you "only rub when backing up, and at full lock? I'm pretty sure I could squeeze a 37x13.5x24 on 24x12 wheels on my Yukon XL, and all I have is a 3" key and spacer lift. Now, I might only be able to turn from the standard 12:00 position to 11:00 and 1:00 respectively, but they would technically "fit".
I'm not bashing you at all, so please don't get butthurt. I'm pretty sure what the OP was asking was what the biggest tire is that he can run without having any interference or contact under all conditions.
285/75/16's all day, provided you have a "correct" wheel width and backspacing, typically a 16x8 with a slightly positive offset. No binding or rubbing under any movement or cycling of the suspension, at full droop or compression. 295/75's, maybe... 305/70's, maybe.... 33x12.5's, maybe...