You did right starting him on the .234 Win. But I see it as a very good deer caliber. What exactly is it that you want that the 243 won't do? Big mule deer, black bears, elk?
If that's your ticket I'd recommend the 270 Win. 257 Weatherby, or 7mm Rem. Mag. In my experience those three represent a step up in recoil above the .243 and a huge step up in game killing. They will do just about anything at reasonable ranges. The larger calibers and bigger cartridges offer lots more recoil with little more effect on game.