Well browning had made the BLR in 358 and I think they still do. I do not know about the 338 Federal
Henry might consider doing one as a custom job, Especially if you were to send them the barrel blank.

So before you make your decision I'd suggest you call both of the companies and talk to their shop managers or custom order departments. You may find one or the other to be more accommodating then you thought they would be.