Why not just go with the match primers (unless they cause a problem)? They don't cost that much more, and are more consistent. I bought 1000 of the Fed 215 Match and have been happily banging my way through them with my 338WM(soon to go bye bye), 338RUM, 7STW and 264WM.
I have been shooting Rem 9 1/2 primers out of my 243 and other standard calibers. I don't know if this is the best primer, but several of my guns including the 243 shoot great (.5 moa or better). I bought 3000 of these primers, all from the same lot.
This is not one of the usual powders, but my 788 243 shoots .5 moa or better with the Hornady 87 gr BTHP in front of 33, 34 or 35 gr of Win 748. This is a mild load, around 3000 fps. I just tried it once because I had some 748 laying around. I've shot several ragged hole groups with it at 100 yds.
For your 338, www.midwayusa
has Combined Technology 230 gr Fail Safe (blemished) on clearance for $9.99 per 50. I ordered a couple of boxes. Not the best B.C. (around .385 I think), but for short to medium range shots should be wonderful on elk and other big critters.