Don
I agree with Don. I've found no need of small base dies with a BAR in .270. If your reloads are not so hot that they give significant head expansion, then small base dies are usually not necessary. But each rifle is a rule to itself. Try some moderate loads for function loaded with your regular dies, and if they give you any trouble, buy a small base resizer.
I have found that the BAR doesn't like extremely slow-for-caliber powders which tend to have an extended pressure curve and therefore have higher pressure at the gas port. I wouldn't use anything slower than perhaps IMR-4350 with your .338 BAR.
By the way, this doesn't sound like a grouse and hare gun to me!
Enjoyed the comment that it isn't a grouse and hare gun. I had carried 338 bolt actions around the woods for 20 years. Lost my feeling of comfort a few years ago when I encountered 3 grizzlies that were apparently hunting me. We all survived fine although I got a much closer look at them than I wanted. They finally stopped at about 12 paces and I had started saying "whoa" as soon as I saw them (at about 25 paces) coming toward me. I had been taking an afternoon walk in late Fall. A couple of inches of crusty snow, lovely scenery, and I was just enjoying the view up the valley. I heard what sounded like a bird dog quietly working back and forth in the alders up hill from me and was wondering if I was in a time/location warp and thought what a strange location to be hunting with a bird dog. Then the first large brown head emerged from the alders. The bolt action felt more comforting than a baseball bat, but depending on (probably) one shot at three large animals at very close range suddenly didn't seem like a good idea. Hence the autoloader, which surprisingly shoots smaller groups than the Ruger, Browning or Winchester bolt actions did.