I think a 21 inch bbl .338 would be interesting to work with, especially if you forgot about it as a ".338 Win Mag" and rather targetted performance to equal .338-06 with a longer barrel.

As such, I think using powders of the faster-for-caliber range you should do OK. Maybe make it something of a .318 WR {ballistics-wise}.

Maybe go to a 20-inch or even a smidge less. Put up with some muzzle blast.

Maybe not my favorite idea, but nonetheless an interesting project.