Hello all, RON L here
I hate to "Parrot", what my fellow members have said here, But I feel they are dead on, a Good Tuned AR with 62GN and a other than 1 in 12 twist should be able to serve your 300 yards and under needs quite fine? Yes, While I do prefer 308 and 3006, In an AR the 223 with the right ammo will serve the needs you have identified! Get some better ammo and give it a Try, then let us know, OK?
RON