Chuck,
If your rifle is bedded and has both front a rear crossbolts, it'll be fine. I'd have it bedded and double crossbolted if its not ... you'll notice a significant difference between 375H&H and 470Lott recoil wise. I had a CZ550 in 458WinMag that was a pussy cat until rechambered to 458Lott and it really came alive at velocities above 2200fps with 500gr.

My current 470Capstick is a sub-9lb Rem700 ... I'll be weighting it up to 10.5lb and adding a recoil reducer as its brutally fun to shoot! You're going to love the Capstick!!
Cheers...
Con