How about a 3 & 1/4 inch 405 Winchester BASIC case formed
into a straight .375 cal. piece of ammo? Bullets 350 grain down
to 270 grain, 2400 FPS for the heavy bullets up to 2600 fps or
so for the lighter ones? Fired from a Farquharson actioned rifle
the pressure should be within a safe level, right?

I thought about that but the 375 flanged is the same performance. It would look cool though.