I have several suppressors, and have fired some larger guns with the Banish 46, which is for the .458 bores and smaller.
Not sure of the weight of the rifle, probably over 10.5 all up in the .458 Win I shot, but in the big bores the recoil reduction is significant. The sensation is very strange and feels like a long slow push . The feel in smaller higher velocity calibers is a quick snap, but the large bores everything seems to happen in slow motion and a suppressor exaggerates this feeling. The 375 H&H should be similar, but slightly less.
Not sure of any numbers, but my brain tells me 20-25% recoil reduction, but a little longer dwell time or push time.
With wider field of view low magnification scopes, you are going to see a big bore suppressor in your field of view. No getting around the fact that they are a good bit larger than a 30 caliber can. Whether your irons would clear a large diameter can might be an issue.
Another issue with big bore suppressors is the amount of powder burned. A normal 308 Winchester burns about 45 grains of powder, while the bigger bores often go over 120 grains, or 3X as much. Wear on the baffles and cleaning frequency are increased dramatically.