Even after running or using standing stance my sight picture is very stable, but when I take a shot the round goes all over the place.

There are a couple of reports about weapon accuracy already but I wanted to point out that specific problem with minimal weapon sway not giving you a good idea of how accurate your shot is going to be.

Also, using a bipod when prone obviously improves shot accuracy a lot, but it's still not as good as the stability of the sight picture would have you believe.

M4 rifles should be pinpoint accurate up to 300metres and fairly accurate up to 600. 7.62x54mm should be pinpoint at least up to 500m and still fairly accurate at 7-800m. If you have the range correct and a stable view through the sights then shots at these ranges should always hit IMO.