I'm not sure which smith you're using - but I'm going from Steve Baldwin's prices at Mechanical Accuracy. So far, he's proven to be a very good smith for long-guns based on reviews from those I trust and from personal experience. I doubt he'd charge more than $300 for just a barrel install, chamber check/cut, and action blueprint (and that's guessing that .338LM would be higher than my .308 was).
I just pulled up that info as a reference. I don't know the guy; but it doesn't seem that far off. If Mech. Acc. can do a full blueprint job for $300, I'd say great.