From a gunsmith's perspective. I've never had a client complain about a Shilen I installed. All my benchrest guns wear Shilen. I have had just as good luck with Pac-Nor, and they are cheaper than Shilen. I had one complaint about a Lilja, and to be honest that sucker was a PITA from the moment I put it into the lathe... but in all fairness I have seen many a Lilja shoot very well.
But you said EXTREME accuracy and to me that means smaller than .2" groups. For that kind of accuracy, the Shilen SSSM #7 LV in 13.5 twist 6mm is the choice. If you keep up on the NBRSA and IBS match results, it is on at least 50% of the competative rifles and takes the lion's share of trophies. Chambered in 6ppc with a .262 neck, of course
That being said, the gunsmith has to do his part, keeping the chamber TIR to less than .0002, cutting the tenon and threads true, etc... and for EXTREME accuracy the action should be a glue-in to an LV stock. That action should also be a custom, or a printed and sleeved rem 700.
Now for EXTREME accuracy in a varmint gun? Get any of the barrels listed - the barrel will not be the limiting factor, the stock, trigger, and action will.