If your going to build a 1000 yard rig, Build one, if you want a Hunting gun that will also work to 1000, you already have one.
A 1000 yard gun is going to need a heavy barrel, a Stiff stock that rides the bags Very well, and is bedded, a trigger that breaks at a few Ounces, a 15 - 20 MOA Base, and Quality Optics. You will not see a Mueler on many Long Range guns...
If you want to shoot
WELL at 1000 Yards, Add in timing and trueing the action, LOTS of work reloading to get "THE" Load LOTS of range time, with a Great log book of every shot. It goes from Fun to Work real Fast...
Your .243 will get you to 1000 with a Good Scope and a 15 or 20 MOA Base, your factory stock etc, you will be able to ring the gongs. at 500 - 600 yards you can do Very well with it