Building a 400yd utra-lite rifle sniper rifle probably will not give you the accuracy you' re looking for. The under 6lb Ultra lite type rifle normally has a thin barrel, skelatonized action and very light weight hollow stock. None of things are helpfull to have in a rifle when accuracy is the over riding concern. Sniper or varmint rifles usually have heavier contour barrels, solid strong actions and a heavy rigid stock.

A 308 is fine. There are several excellent match grade 30 cal bullets on the market.

Good luck in your pursuit but you' ll likely have to make a few comprises in your new rifle.