Whatever you have in mind will have been done already by H&H, Purdey, Jeffery of Rigby. They have been field tested and have stood the test of time.

Here is the list of British cartridges that will meet your criteria from lightest to heaviest.

400/350 NE.

.360 No.2 NE.

.369 Purdey

.375 flanged

If you fancy an American cartridge then I suggest:

.35 Winchester or .405 Winchester.

You can see a picture of these at:

http://www.new-kynoch.apt-sites.com/cartridge%20range.htm#