If no .338/06IMP due to being too similar to a .375H&H, then most of the .375 flanged ctgs. must are too similar to the H&H as well.

That bring us back to a round that would be fun to shoot, of lower power than the H&H to be notable Hmmmmmm The suggestions for a .375 Winchester which (in my own Big Bore M94) makes quite excellent use of .375 Win, or .30/30 brass blown out, can drive 300gr.cast or jacketed to a good 1,650fps or if wanting more speed, a 220gr. FN Hornady to 2,200fps. It would make a fun pig/deer gun and in the similar power range as the .358/.356, but with a bit less recoil. I didn't get around to shooting any deer with mine, but did collect 2 moose with it, using those 220gr. FN's running 1,940fps driven by 42.0gr. H335 - a low pressure, but VERY accurate load(1 1/2MOA 100yds.) - obviously having sufficient "power" for 'up to' 800 to 900 pound ungulates.

So many choices, so few actions!