While a Cooper is all you pay for in a gun(good investment), your cartridge choice makes no sense for the application.
243 AI, overbore barrel burner, overpower mid range hunting.
6x284, Same taken to ridiculous.
6.5x284, long range barrel burner, not for hunting junk at a landfill.
Cooper's wood stocks are bedded -without pillars, and they're HUNTING stocks(not BR). For this application, I suggest you look at Savage model 12(target) in 6BR.
Savage Arms > Firearms > Browse Models
But call them & ask for a slower twist barrel for mid-weight FB BR bullets.