If the Winchester action (which is not magnum length) will work, then the Ruger "long" (not magnum) action should also. They advertise a left hand stainless/synthetic in .338 magnum; I'm sure one of those will be much easier to find and quite abit less expensive than the Winchesters.

If you don't mind proprietary cartridges, I think they are going to make the stainless .375 Ruger in a left handed version.