Sounds like you have some kind of issue going on with that resize die. If factory ammo works and don't stick but what you size with that particular die does that seems to point to the die. You already have the die camming over so it wont "bump down" much more at this point. You can continue to screw the die in and get to the point where it almost wont cam over without damaging the press but the case wont come out no different.
I would suggest you try two things at this point...one, try cases that a buddy has resized with his die to eliminate the die you have, and two, load a few minimum loads and try them to make sure it's not some kind of hot load thing going on. The loads you listed seem a little warm. You do not mention any signs of excess pressure.
The only time I have ever had a case stick in the chamber of an AR was when the rifle had a bad, rough or chattered chamber. In your case factory ammo works fine, so that kills the rough chamber idea.