308sako,
are you using the sako stock?
i shoot alot with the std 461/579 stocks and they are not easy to use on the bags like a BR stock is, being the butt is sloping very different to the line of flight, unlike a BR stock where they are more parallel, also the fore end is rounded on the edges, so they rotate some what.
if you are using this style of stock, make sure the cheekpiece is clear of the ears and try a little more forward pressure when firing, being the opposite to free recoiling
i have little experience with BR shooting, but i think it is a technique that suits your setup, you are chasing
best of luck
JB