koivu: When you said 'shoots ok', what did you mean?
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If your barrel is the original mil-spec barrel do you recall the number on the stock disc which indicated the amount of wear??? I ask because even the #3 barrel on my sporterized M38 puts three factory rounds into one hole from the bench.
You provided that you added a new stock - is it bedded?? Mine shoots better with a free-floated barrel and bedded action. I have not yet began reloading for my 6.5 as it is so very accurate with factory ammo and I prefer the Sellier and Bellot 131 gn soft point for my hunting loads or their 140 gn fmj for plinking.
Also, have you checked your barrel or scoped your barrel to see if you have any copper fouling buildup as that will hurt your accuracy; you can often see telltale copper deposits or copper 'streaking' on the rifling is buildup is evident.
Howsoever, if you feel your barrel is simply shot out I would replace it with another 6.5x55 barrel and not go with any caliber changes. JMTCW.