Re: 375 H&H
no semiautos that I've heard.
375H&H headspaces off the belt, the shoulder can't support it. I'd go with a 375 RUM or 375 Ruger. I headspace my 7mm Mag off the shoulder. H&H uses magnum action. The Ruger uses 30-06 (long action) with magnum boltface.
If you stay with H&H, try...