If you handload, buy the .243 and have it reamed to .243 AI. The performance will be enhanced enough to get you the 6mm zip you want and still be recoil friendly to anyone. You can shoot factory .243 out of the improved if you ran out of ammo in a pinch.
Accuracy with a 40 degree shoulder seems to be a bit better than the standard 17-28 degree cartridges. I'm not exactlysure why, but it is. It may be headspace and datum line stuff, but someone on this forum could answer better than I.
Just some comparison data:
75 grain bullet .243 Win .243 Win AI
46 gr of IMR 4350 =3415fps50grains 4350=3765fps
A little more powder capacity and 350fps faster.All my improved riflesshoot MOA or better.The best of both worlds can be achieved with improving a cartridge. A safe increase in powder capacity( 5 to 10% more)yields more speedthus flatter shootingfor a bit more distance if needed, more energy and accuracy that exceeds the normal factory production ammo.
A competent gunsmith with experience inthis aspect of re-reaming to improved canmake your rifle be more than you expected.
Good luck!