You know you don't need a .375 H&H for Sitka deer.
Don't you have a 30 caliber already ?
If you really want a big bore why not look at that 416 Rem Mag (Modern day .375 H&H or 416 Rigby).
http://www.reloadbench.com/cartridges/416rm.html
Really just looking for an excuse to buy a new toy huh !!!
Buy one of those high end scopes and put it on one of the rifles you will use more often !!!