I have a 2015 Sierra All Terrain, running a 2.5" Rough Country level and Toyo AT2 Xtreme 295/55r20 (33x12) tires on the factory 20" wheels. I know the factory AT and Denali wheels are both +27mm offset, it's stamped right in the back. I'm assuming the Chevy 20's are also the same. Saying the MAX tire size you can run is kind of irrelevant because a 305 Mud Terrain is going to be wider than a 305 Highway Terrain, and no brand is exactly the same size.
What I can tell you for sure, is on stock +27mm offset wheels you WILL rub the control arms with a 305/55r20 (33x12.5) wide tire. Everyone is always concerned about rubbing fender liners but that's plastic that can be easily manipulated. The control arms and sway bar are however a little less forgiving if you're rubbing up against them.
Here's some pictures of my truck:
You can see where the sidewall rubs the UCA and sway bar at full lock. I know of two other forum members with the exact same tire on factory 20's with the same issue so I know I'm not alone.
Seeing that the 295's rub, I guarantee the 305's will... It's the wheel offset thats killing it, many forum members are able to run the 305's with no clearance issues by simply running an aftermarket wheel with +12 or +18mm offset.
For sure you'll clear 275/60r20's (33x11), I've even heard of guys running 275/65r20's (34x11) but they might slightly rub the inner fender liner that can be zip-tied back. I'd be willing to bet that a 285/60r20 (33x11.5) wide tire would be the ideal size to clear the fenders and control arms, but pretty sure that size is only available in the Goodyear Duratrac's.
Another thing to consider if you care about fuel mileage is tire weight. Initially I thought I could fit 295's or 305's and only decided on the 295's because their 14lbs lighter per tire when comparing the 33x12 to the 33x12.5.
I'm going to try and add some 8mm front wheel spacers to simulate a +19 offset wheel and see if it's enough to push my tires out far enough to clear the UCA's.
Crawl under your truck and see what you're wheel offset is, it should actually say "20x9 +27mm Offset" or it might be one big number like "20x9JXIS27", either way knowing your offset is crucial to figuring out "what fits or not".