It's been a long time now since you started this thread and you've not told us what you got if anything yet. So what did you get?
I think the .338 Federal would do fine for what you have in mind but then so would a lot of others such as the 7-08 or .308 Win. as would the .270 Win., .280 Rem. or .30-06.
I once got the hots for a Kimber Montana in .260 Remington. I called to ask what accuracy might I realistically expect from it. The rep at Kimber refused to give me a straight answer and all he'd do is make excuses about I shouldn't expect light weight rifles to shoot as well as heavier rifles. I've owned far too many pencil thin Remington rifles that shoot consistently less than inch groups at 100 to buy that BS. I wound up buying a Model Seven Remington in .260 Remington instead. They could have made the sale by merely giving me an honest answer assuming that answer was around an inch to an inch and a quarter.
His refusal tho made me think it might be more like 2" or more and that just wasn't acceptable to me.