.458, really nice rifle!

An Improved .38-56 {not .38-55} would be perfect. Take some taper out of the .38-56 {.45-70 basic case} and blow out the shoulder, set it up for .375 diameter bullets and you would have a round approaching the .375 Whelen that could be made up in a very light rifle.

Ken Waters' .375 Express or whatever he called it using the .444 case looks go, too and would likely be easier to get the rifle to feed, but would I think give up a bit of case capacity.