Couple of things.
1.) First - the 243 is not an elk cartridge. I have seen it take a cow moose at close range. It was with a 95 gr Barnes X and a real stiff load of H414. Blew a rib back through the lungs. Moose went about 30 feet before piling up. My wife was the shootist. She asked me for a bigger rifle on the way to the downed moose. I gave her one.
2.) I cut down an old 30-06 Tikka to fit my wife and daughter. It is now their rifle. It doesn't fit me anymore. I started looking at ways to reduce the recoil without sacrificing performance. I settled on a 150 grain Nosler Partition bullet at 2800 fps ahead of a 46 gr charge of IMR3031. It shoots 1" groups at 100 yards. Virtually NO recoil to speak of. Both my wife and daughter shot deer this year. Three shots fired - three perfect hits at 190 and 195 yards. By the way, they are both 5'4" and around 120 pounds.
I would recommend for you to do a little research before getting a too small cartridge for a too big game animal. Sure, they may work under ideal conditions, but conditions are not always ideal.
Common sense would dictate a different cartridge. But the common sense is not all that common anymore.
