As far as the 308 to the 338 goes , it can be done on your action but you will only be able to shoot it in single shot form and will probably have to pull the whole bolt out to get a live round out of the chamber.
Now as for the 308 to 300WSM , that is a pretty easy conversion.
Cheap way: have your barrel rechambered to 300WSM and replace your bolt head with a Mag bolt head , and if you want it to feed from the magazine you'll have to have the lips opened up
Best way: Send you action to Kevin Rayhill and tell him what you want.
I had a 308 barrel rechambered to 300WSM for a 110 action , worked great as a single shot and semi ok as a repeater with a mag sized magizine , the rounds wanted to jump out of the action sometimes though , this is whay Savage uses the controled round feed bolt head on their WSM but you have to have a special plunger made into your action for this head if your gun isin't already a WSM as it doesen't have a spring and plunger type ejector.