Well since you already have a "338 something" i would go with my two favorites. First the 7mm STW. You can push a 168g Berger bullet over 3200 fps and take any north american big game with this cartrage.
Second i would go with the 243 Super Rockchucker. It is a 25-06 case necked down and shoots a 243 bullet. I am shooting the 90 grain bergers at 3600-3700 FPS. Although sutible for deer sized game it really shines on varmits. I would not consider this to be an extreame wildcat. If you handload there is nothing to it.