The straight .303 to .408cal is an interesting number.
It is a little shorter than the .40 Maynard, seems to me and would make an excellent smokeless round for a Mark 111 or better yet, a #4.
Ken Waters, some time ago, had a #1 Ruger chambered for the .303 necked to .375 and called it a .37 Rimmed, seems to me.