If you want to stay with the 08 case, 338 Federal would be a good choice for you "third" barrel. It is the ballistic equivalent of the 338 JDJ#2. I have one in the FA single shot & it is fun to shoot. Alternatively, as suggested above, the 338-06 will give you a little more velocity (and power) at the cost of additional recoil. Might even go ahead & get a 375 (JDJ or other) if you really want to move up.
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It's more important where you hit 'em, than what you hit 'em with.