Amazing.
I take it this means the case is a necked case - perhaps a .444 Marlin case might work as it is also 2 1/4" in length?
Rim dia. is listed as 13.1mm (.514"). Body .4706" at the base (11.95 mm) The rimmed 7x57 as well should be about the same size as the .444 Marlin.
Or is this too large in dia.