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6mm BR Issue

Have an old Savage rifle, re-barreled with a 6MM BR Shilen, 8 twist. Tried a variety of bullets and settled on 108 Gr Hornady eld-m and Berger 109. At 100 yards, the Berger 109s group better (3s, occasional 2s) than the Hornady 108 (4s and occasional 3s). 1000 yards is were we see a real difference. My wife and I shoot in Global Benchrest Association matches. We are not serious competetors, mostly compete for fun (you know, $400 Savage against $10,000 custom light guns. Match days consist of 2 matches. My wife shoots the Savage. She shoots the Hornady eld-m in the first match and the Berger 109s in the second match (still trying to determint the best bullet). Surprisingly, the Hornady 108 outshoots the Berger 109 at 1000 yards, consistantly (at 100 yards, results opposite). I believe the 8 twist is giving the Berger 109 marginal stability that doesn't show up at 100 yards. In one match, my wife actually won her relay, with a 5 inch group (beating the $10,000 rifles, made me smile) with the Hornady 108 eld-m. Best 1000 yard group ever with the Berger 109's was 7.5 inches, which I believe may go back to bullet stability. Might need a 7 twist for the Berger 109s.
 
Guys. I have a 6mm BR that currently has 220 rounds thru it. I have worked up loads with both the 110gr. Hornady A-Tip and the Berger 109 gr. Hybrid Target. I’m using Lapua brass with the necks turned to 0.125 which cleaned up about 85% of the necks. I have loads worked up with Varget and H4895 which will both shoot groups in the 2’s. My problem is that every load that will shoot this well will put 4 rounds into a 0.2” or 0.25” group and then throw one round out that increases the group to 0.40 or 0.50. It’s never the same shot but it seems to be consistent at throwing one round out of the group. It could just be my shooting, lol, but even a blind hog finds an acorn on occasion so I believe its an ammo or rifle issue. The rifle is a Rem 700 action with a Preferred Remage barrel in a laminated stock that has been pillar bedded. I haven’t bedded the recoil lug yet but I just don’t think that’s going to cure these flyers. I checked the Varget load and it was running an SD of 6 so I don’t think it‘s a powder problem. Any suggestions on what to try next to remove these flyers would be appreciated.
What is your barrel twist? Could your issue be marginal bullet stability?
 

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