Quite a few years back, I managed to fire 200's, with a decent x-count, on the 300m ISSF target, with a 303 British I built on a P14 action. I also shot three consecutive 5 shot groups, all under 5/16" at 100m. A few weeks ago, with the same rifle but now with a 30 caliber barrel, I shot a ten shot group at 300 m which measured just under an inch. So the P14 can work. This action is modified somewhat. A welded in solid bottom, 5/16 striker travel, and a three lever trigger, are some of the changes. The barreled action sits in a laminated stock.
Using anything other than a commercial precision action is a bit of an uphill battle and there is little reason to do it unless, like me, one enjoys the building as much as the shooting.