Hey Bob
Get yourself an inexpensive but decent, middle of the road (recoilwise) gun (like a Rem 700 ADL)...and practice alot with it. I don't care what anyone says, shooting that .340 will hurt after a few shots. I agree, it would be very easy to be kick shy on a gun like that, especially if you spend much time shooting that .222.
I think if you spend some time on the bench with a medium recoil gun, you'll gain the confidence you need to shoot that .340 accurately. Good luck.