I don't have a Chevy, but maybe my info can help you plan.
I tow a 303 with a 14 SB CC F250 FX4 with an AUH connected to a B&W Turnover Ball.
First data point is I'm really happy with the whole setup.
Second point is I have 2014 303 which may be a bit lower at the pin than yours.
When I went to pick up the trailer, I had the ball at the highest position and the ball socket in front of the king pin. I was a bit nervous about clearances thinking cab clearance would be my biggest problem, and I had to pull out onto a very winding, hilly, narrow 2-lane for a mile, then got onto a busy 4-lane so I was hoping I'd made the best "safe" choice since there was little option to stop and make a change until I was 6 miles or so down the road. It towed fine, but it wasn't optimal. Once I got home where I could look more closely and do some slow speed turning in my front field, I could see that the ball socket forward position wasn't best since it put the bottom of the pin box close to the bed sides when turning sharply. When I flipped it around, I had much more clearance on the sides, and was still able to turn 90 degrees. The extra side clearance also made it possible to drop the ball to the middle position for more level towing. I believe I'm still about 3 or 4" pin high when towing, though I haven't had a good opportunity to park it on a flat slab to look and measure more closely.
I still have the notes I made with height and distance measurements from the gooseneck ball to the cab, tailgate and sides, and I'll try to remember to post them later so you can compare your dimensions.
BTW, I recommend adding a mat under the hitch. I used this one
https://www.tractorsupply.com/tsc/p...t-black-4-ft-x-3-ft-x--frac12-in?cm_vc=-10005. I cut a hole to give access to the gooseneck ball and safety chain ties in it. The hitch made marks in the factory bed liner on my truck, but they went away after sitting in the sun. I added the mat as insurance against permanent marks.
