Welcome to the site.
To start I think you have a good start of a great set up. I am guessing your talking about shooting at 100 yards, and 5 shot targets. You should be able to get a tuned Savage with a good barrel to consistently shoot in the .2's and better. There is a lot of information missing for your question. What type of stock do you have? What kind of rest and bag set up are you using? What type of scope? What is your experience level? Are you using wind flags? How many rounds have been fired down the barrel? What weight and type of bullets are you using? What twist rate is the barrel? These question will answer a lot.
I would say that most times a person is having accuracy problems is it do to a bad scope, or the bases and such are not tight. There is a common problem that some base manufactures include screws that are too long and will bottom out against the barrel, (On the front) not allowing the base to get tight.
The 6BR is a great round, and it seams that Varget or Reloder 15 is a great choice. Many shooters use and report having the best luck with either Remington 7 1/2 primers or cci 450 Mag primers with this round. Lapua brass is the best, no question about that. Have you length trimmed them? I have seen a lot of rifles wake up by simply trimming the brass.
A few other questions that come to mind when the barrel was installed was a good aftermarket recoil lug used? A lot of people will ask what kind of dies you are using and I have found that most dies are good. The main thing is to check consintrisity of the loaded rounds.
In closing I would say that you are not asking too much, I would be looking for problems if the guns shot in the manner you are describing.
Gust for reassurance here is a few common groups out of my 6 PPC Savage.
[img width=415 height=450]http://i34.photobucket.com/albums/d145/82boy/scan0004.jpg[/img]
[img width=497 height=450]http://i34.photobucket.com/albums/d145/82boy/scan-1.jpg[/img]
If you still need convincing this is a group I shot and won a single match at the 2010 IBS 600 nationals, with a rifle that is dang near what your describing. There was several match's in the 2 inch area that this gun shot that day.
[img width=600 height=437]http://i34.photobucket.com/albums/d145/82boy/IMG_0455.jpg[/img]
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