I disagree on the cost. Classic Barrel Works in Prescott Az easily beats the cost of a new barrel.
While I haven't had this particular combination done, I did have a 30" #7 lilja SS 7mm barrel rebored/rerifled to 338. Dan Pederson did this for approx $225.
Funny you should ask about making a 338 Edge, as I have a 27" #5 fluted SS lilja in 300 RUM with a Vais brake that is getting tired. When it finally goes I will make it an 338 edge. The savings will be significant compared to another fluted barrel with muzzle brake
Here is his website: Classic Barrel Works