Alex

You need another medium bore no less, to build a nice light stalking rifle. A single shot stalking rifle needs a long slender cartridge.

That means todays modern classic the 9.3x74R. The heavy bullets will take any deer you want in the thick stuff and the light bullets can be loaded for long shots. but you already have your little double in this caliber so that means the classic 400/350 Rigby which has been mentioned a few times already. 310gr bullet for heavy work and 225gr bullet for the open. This gets my vote but may be too close to what you already have.

The Holland 30 super flanged would be ideal.

But why not try something different.

375/303 Westley Richards
Factory loads
200gr bullet @ 2726 fps
215gr bullet @ 2500 fps

I believe it is similar to the 375 FL NE 2"1/2 case necked down to .303 with a smaller and thinner rim. You can load lighter bullets. It nestles nicely in between your other calibers. The only issue may be brass availability in which case you could opt for an 8x65R which is a similar case and performance except it's not a NE so it's not as sexy :-)

Cheers
Rhodes