Up until a couple years ago I had a Ruger M77 MarkII Target in .243 with a 9 twist barrel. It shot both 87gr V-max's and 90gr SST's very well, but it would not stabilize 107 SMK's. 9 twist is borderline for anything above 95gr IMHO. It's kinda like shooting 69gr+ bullets in a 1-9 twist .223. Might work....might not, but I aint gonna bet money on it. Now the 1-8 twist barrel on my 6BR is a different story, all I've ever shot out of it is 105gr+ bullets.
Don't get me wrong...I love the .243 Win. caliber. That Ruger of mine has taken antelope at over 600 yards, but I would never recommend anyone taking game shots at that distance without lots of range time and many rounds downrange shooting those distances in real life. Hunting is not the time to find out if the ballistics chart you ran on the computer with estimated figures is correct or not. Nor would I take that shot, with that rifle on full size whitetail. Antelope are very light skinned, thin boned game and pretty much tip over if you throw a rock at them. Deer are a lot tougher, elk and moose are off the chart in comparison. Like others have said here range time is far more important than caliber selection for taking long range shots on game. I've always liked the paper plate rule.....if you can't put 5 rounds in a row in an 9" paper plate shooting X yards from field positions you shouldn't be taking the shot on game. Cuz if ya can't hit in on the range it's highly unlikely you will hit it in rugged terrain, at altitude with your chest pounding and your adrenaline surging.
Personally, knowing that the OP is planning on shooting factory ammunition through a factory rifle I would suggest something a little bigger than .243 if you have high hopes of dropping an elk at 500+ yards. One I haven't seen mentioned yet is the 6.5 Creedmoore which is a fantastic cartridge and being offered by many of the major manufacturers these days. That's about the minimum that I could recommend. Next would be the .280, 7mm-08 or .308. I don't really have much love for the 30-06, since the .308 can pretty much keep pace with it in a short action. If you feel the need to go bigger you might as well jump to 7mm Mag or .300 Mag.
My personal tool of choice for big game hunting is a custom 7mm Rem Mag. shooting Berger 168gr VLD's. Rifles are like people, everyone's idea of the perfect specimen will vary per the individual. Here's my ultimate hunting rifle, keep in mind most my shooting is done from 400-700 yards out west....... so this is not what I would pick for hunting the thick woods of northern MN. This rifle easily shoots 4" groups at 600 yards if I do my part.
7mm Reminton Mag
Squared and blueprinted Remington action
Jewell trigger
26" 1-9 twist Kreiger barrel in a custom heavy sporter contour
Holland recoil lug
HS Precision thumbhole stock/ action bedded with Devcon
Leupold VXIIILR 6.5-20x50mm scope with target dot
Leupold Mark4 steel rings