300, another potential rimmed case is the 500/416. It's a modern, heavy case based on the 500 3-1/4 necked to .416 with capacity close to the 416 Weatherby/Rigby.
BeLL makes brass and factory ammo is made for the doubles so chambered.
Necked to .375 you should be able to get the velocities anywhere you want from 375 Flanged to almost 378 Weatherby in a modern gun and still have the rim. the 500/416 is third from the right:
[url="http://www.hunt101.com/?p=146181&c=500&z=1"][/url]]500/416[/url]

For reference, left to right:
50 BMG, 550 Magnum, 505 Gibbs, 458 Lott, 500/416, 416 Rem., 300 Win. Mag.
Nice long neck for cast bullets, too.