Also of note, is the .312 Express by Ken. In this one, he used the standard .303 barrel and chambered it for the .350 Rem. Mag. necked down to .303.

Mine runs 2,960fps with a 174gr. bullet in a #4 using Reloader #19 powder.

Please note, the .375 Express by Ken, is quite literally a .375/57 Flanged Improved, with it's .4565 shoulder.

The rifle Ken used, was an original Westley Richards - a #3 or perhaps Lee Speed, I presume using the original barrel. Because of this, his ballistics only barely match what can easily be done in the smaller .303 case, in #4.

As Grenadier suggested, this would also be a really good round for either of your rifle suggestions.

Barely shortened .376 Styer dies could be used for loading this round as a neck die set. I used just such a set of dies (Hornady) for my .375/06IMP now.

9.3x57 dies, with the neck opened up, could be used for the .303/.375 round as neck sizing dies. This, rather than having expensive custom dies cut.