Item #1: Bed and float your Classic, that'll put you into MOA right away.
Item #2: As someone has said, the .223 is really not a long range gun...yes you can hit stuff way out there, but you are looking for enough retained energy to kill stuff.
Item #3: also as someone said many good varmint bullets will get you to 500 yards in a 12 twist. 500 yards is farther than you think......handload 55 grain NBTs and rock on.