Send it to Bits of Pieces in Delta. The whole job shouldn't cost more than $700 depending on which barrel make you prefer. I've used a lot of Green Mount barrels which BOP carries and for a hunting rig they are as good as any for a lot less cash outlay.
OP, Some of the modern rifles being offered today will cost less new than it will to have a high end barrel fitted to your present rifle.
Not sure how difficult it would be to import a barrel from Brownells but it's a good way to go. Pre threaded and short chambered Shilen barrels. Many years ago, (OK decades ago) I did one in 35 Whelen. Back then you could bring in a barrel (and the finish reamer if required) without any import permits. They mailed straight to your door. The barrel was excellent quality ( for a hunting outfit ) and performed VERY well.