I've shot the Sako on BR, I used 11 year old HV PMC ammo, on cheap front and rear bag, it went bang and was more than acceptable for a borrowed rifle with a overly heavy trigger and a cheap scope not setup for my eye.
That said it was more accurate than I was on the day, and even with ancient ammo and poor setup it fired groups just as good as those using top end rests and Tenex ammo.
The Sako's are damm good rifles, their price shows that, good chance the bedding is poor and muzzle has been damaged, it don't take much to make poor groups, and while 5/8" is not the best if put into the middle of the target they would still all be 10.
It's not that exe to add a good match grade barrel to the sako action, it would then come down to the operator not the machinery, I trained a guy once who had a very accurate hard kicking 7mm 14" Thompson Contender, the very best he could do from a sandbag rest on the bench at 25yds was maybe 3".
It would have been easy to think there was something very wrong until he asked me to put 5 through it with his own loads until I put them into a ragged single hole, so it's sometimes not the gun alone.