The biggest hurdle to get past if you want to convert a .308 into a .300 WSM is to get the action properly modified for reliable feeding, and then have a proper magazine box installed that will truly fit the .300 WSM cartridge. The original .308-size magazine box WILL NOT WORK. This is the biggest misconception that a lot of people work under when they contemplate a quick and easy (also cheap) conversion to a radically different cartridge. Rechambering is the easy part of the battel. The sometimes difficult and usually expensive part is in the proper (not half-assed, not jackleg) alteration of the receiver, bolt, extractor, and magazine box to make everything work as it should. This is the part that's tough and can cost some serious money.
Here's the best and most functional, cost-effective solution if you want a .300 WSM instead of your existing .308: Trade the .308 in on a .300 WSM. No other solution makes sense. A factory .300 WSM will have the proper bolt face, magazine box, magazine follower, follower spring, feed rails, etc., already in place. Believe me, the cost of altering a .308 to work as well as the factory .300 WSMs do would cost more than the retail price of a new .300 WSM from either Browning or Winchester!
That's why the trade-in idea makes the most sense, and not only that, but if the new rifle doesn't quite shoot to your liking, you can always have a new barrel installed. The action is timeless.........
Thank you for your comments, and of course under normal circumstances you are perfectly correct. While I have converted many Mausers to "standard bolt face" cartridges, I have never done a magnum. Several reasons, one exactly the problems you mention. Basically, for me, it's a learning process-I would want to see exactly what problems are involved, and work through them. The idea of the .308 bbl is to not have a lot of money tied up in case the project failed! (I am speaking here of doing the work myself, of course, not farming it out..)