With enough money you can do almost anything, but I would look at the economics of what you want to do to see if it makes sense. Estimated costs:
New (quality) Barrel minimum, they go up from there. $250.00
Custom fitting and chambering, minimum, goes up from here 150.00
Tactical stock, SWAG (if available for your action) 175.00
Possible bedding of action to stock 100.00
Modify action for box magazine (Serious machine work, SWAG) 250.00
Bolt Modification 100.00
Value of your current rifle ???.??
Total $1025.00
The above is a cost of $1025.00 without the value of your present rifle and I would question what the resale value of this rig would be if you decided to let it go.
To modify your action for a box magazine is more work then most people would think. First you need to find a magazine that will handle the 300 Win. Mag if you want to stay with the same caliber. Then you will need to machine out the feeding rails from your action, they are in the detachable magazine. Assuming conversion parts are not available from the custom market, the bottom metal is going to have to be machined to allow the detachable magazine to pass with appropriate tollerances and a latch system fabricated. With all of these modifications cartridges must feed properly or it is junk, no cake walk for a one off job. $250 is highly conservative here!
BTW, the above estimates are in my opinion very conservative and you could spend a lot more if you went with a "select" barrel from one of the top of the line manufacturers, etc.
While I am not a fan of the looks of Savage rifles you can buy one of their tactical models for half of the costs of the modifications above and have a darn accurate rig that you can sell for close to what you have in it if you ever want to sell it.
Just my $.02 worth!