If all you want to do is shoot 300 yards with a .223 just buy yourself a Varmint rifle of your choice, add a good scope and shoot to 300 yards.
IMO this is what you do . 300 yards is nothing to shoot . Almost any bolt gun will do this well . I shoot .80 MOA with my $360 Ruger American rifle @300yds .
Yes It would be fun and would help on the next build but a hole lot of money can be saved by getting someting stock and seeing if you really want to move foreward . There is SO much more to shooting long range then the gun .
I'm in no way trying to say what you want to do is wrong , cus it's not . Just want to give you other ideas to consider .