.303 brass can be cut to suit .416 for sure and I have an old article on the .44 Rhino which was a long cylinder revolver using cut off .30-40 Krag brass so .303 brass should do the same. I can't recall if the brass was reamed after trimming or not.
I was considering the Lee Enfield in .444 Marlin some time ago but never got to it. If I were to build one now I'd go .45-70 or cut off .30-40 Krag or .303 British for a wildcat round mostly because .444 is expensive and not common here and brass even less common but .303 is readily available. Of course things may be different where you are.
Another option is the .444 rimless based on .308/.30-06 brass head size. Likely need a different extractor in a Lee Enfield action though.
Not that there us anything wrong with the .303-.375. For me, I have lots of .44 moulds so I'd lean that way.
Different strokes.
Longbow