Richard just sent me some Bonded Core .338" FB 250 gr bullets to test out. THese are built on the 0.040" jacket. They are over at the shop right now but I will try to remember to bring them over later and take some pics and post them. Serious looking bullet but For anything but extreme close range shooting or extremely heavy game, I would bet Richard would recommend the 0.030" jacket for everything else.
Drop him an e-mail at firstname.lastname@example.org
and ask Da Man his opinion. He is more then willing to offer all his experience. From what I have seen the 0.030" would be the jacket I would use in the medium 338 calibers like your Wby for any game from Moose on down.
If I were hunting Brown bears or Polar bears I would go up to the .040" jacket and probably up in bullet weight as well to the 275 gr.
For African heavy game I would also choose the .040" jacket.
Richard sent me a blank, unformed 0.065" thick jacket to look at, ain't much lead going to fit in that pill. Will post pics of that as well tonight or tomorrow.
Drop Richard an e-mail, great guy to talk with!