I have 200 Grain Sierra Pro-Hunter and 225 Sierra Game King(discontinued I think), and taken deer with the 225 at short range, under 100 yards. Very pleasant, less blast and recoil like a .243.
Heaviest I have are 300 Hornady InterLoc.

350 (Sierra Match King) and 375 grain are made for the .375 CheyTac but I have never seen or heard of anyone using them in .375 H&H nor have I ever seen loads developed for the 350 grain from a respected source.

Rell indicates experience with the 350gr Woodliegh.

The CheyTac has 'moved your world' of .375 into another dimension. Having fired both .408 and .375 CheyTac the experience is.....different.