Gerry, E.R. Shaw barrels have been around for quite a few years. They are not known as being the best quality barrels. I have used a couple, one was so-so, and the other was excellent. definitely they are not in the same league as Lilja. Who ever sold you that rifle and told you it had a Lilja barrel was just out to "skin another unsuspecting soul". Lots of folks like that. Only advice I can give is what Karl Kenyon once said to me after I was "taken in" like you. He said," If you ever see that guy coaming again, turn around and walk the other way."
Some Shaw barrels will shoot well, it is just the cost difference. If it groups good, just shoot it and tell yourself it's doing what it is supposed to do.
My experience with all the less expensive barrels is that they need to be bore lapped so that they don't copper foul. Once lapped most all shoot well. Don