Several items in the post raise red flags. "Bore looks good but it appears chamber is cut very crooked in relation to bore." A little cerro-safe and some measuring can confirm this. Go guage doesn't fit. Is it a 5.56 Go guage? Or is it a .223 Remington go-guage? They are different, however slightly, they are different.
"Handloads I have to turn my size die down until the press cams over to get it to close on them." If your dies size your brass so they fit the gun, what is the issue? You don't shoot the go-guage. If it doesn't fit is really a moot point if ammo fits.
Have a bore scope? I would bet you have a burr in the chamber. Check your brass to see if any marks in the neck that could possibly be cause by a burr. You might also get some .223 Remington ammo and some 5.56 ammo and see if one fits better than the other. Again, minor differences, but can seem like big problems.
Steve