You clearly made some headway by tweaking the bedding as the big fliers are gone. If your not shooting over some type of wind flag, it's pretty tough to know whether the horizontal is real or not.
The horizontal with the Berger stuff is actually good to see....shows that the barrel will tune. The Berger stuff just needs more or less powder to get the vertical out. It also shows that the barrel responds to a good bullet.
As Adam in Wi suggested, giving it some more firing pin springs is advisable on the 'new' Model 70's. Poor primer performance from weak hits can certainly show up on target....sometimes. And sometimes not. But for a couple of bucks, it's cheap insurance.
Factory ammo is always a tough road, especially with a light barreled gun like yours. Honestly, if you don't want to get into hand loading to tune the gun, I'd suggest testing the Hornady 168 stuff some more and if it repeats that performance, buy a bunch and enjoy it.
All in all, 1/2" Model 70 FW is pretty nice!

-Al