I would likely go with something like a 458 Winchester magnum case, or a 338 Winchster magnum case or maybe a 378 H&H too (others in these big size ranges too). These have case sizes exceeding .411 inches. A .308 Winchester case itself is a little on the small side though.

Some of the other big game super cartridges would work too. You could get some big bore rifle case blanks and resize them down as needed too.