The most accurate .308's based on a conventional box magazine bolt action rifle I know of have all been built around a Winchester 70 action but used an aftermarket barrel. Too bad the Winchester factory barrels are not all that great for precision accuracy.
The modern tube guns are probably the best buy for an over the counter super accurate rifle these days.
US Navy Distinguished Marksman Badge 153
Former US Navy & Palma Rifle Team Member
NRA High Power Master & Long Range High Master
NRA Smallbore Prone Master