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Soft Winchester primers and your firing pin hole is over sized for your pin.
can that cause accuracy deficiency?
those are remington primers
Possible contributing factors
-Large FP hole for reliable ignition under all conditions.
-Primer Cups a bit too soft.
-Load too hot for above conditions.
Possible solutions
-Bush FP hole and reshape tip.
-Switch to harder primer
-Reduce Load
You state your loads are "mild" but how do you know they are in your rifle? Can you give details on your load?
I see at least three different headstamps and some .260Rem and some reformed .308Win. That is going to change pressures.
Have you chronographed the loads?
Look up Gre'-Tan Rifles or you can order a oversized firing pin from Pacific Tool and guage.
What does it do with factory ammo? Clean the crap out of everything before shooting it again.
I personally think Remington and Winchester LR primers are softer than CCI and Feds
I had the same issues with primer piercing and primer pockets blowing out when I had a 260 barrel on my AI Aw .kept getting worse and I ended up screwing up the boltface. Try using CCI military primers white box they have a harded cup from what I've heard. Good luck , I hope you get the issue resolved.
according to this
http://www.snipershide.com/shooting/snipers-hide-reloading/141446-ai-ax260-pierced-primer.html
its vary common for it to flow like that in AI's... the only 100% fix is to have the face bushing installed...
as long as im not punching holes in the primers, im not worried about it