As kraig said it's all about keeping it from going subsonic and becoming unstable. I would honestly look to .300 RUM and load some 220gr or 240gr SMKs, or berger 230gr Hybrid, i guess just my preference.
Here's some loads for the 240gr on a RUM pretty decent.
Ripnbst he's referring to ammo.. shooting a .338LM is like shooting 5$ bills. .338 RUM would be a more cost effective solution. You could easily have a .338LM made for much less than buying a AI or Sako. Both of which are known factory .338s that shoot lights out. But ammo like the .50 BMG would run you through the roof if you actually plan to shoot it alot.
"Combined synergy of a man and rifle is matchless, the steadiness of hand and acuity of vision, and finally the art of knowing how to make the rifle an extension of the body, all equate to the ultimate synthesis of man and machine."
"Death smiles at us all, all a man can do is smile back."