I have one of the boat anchor heavy #1S rifles with the medium heavy barrel and the Alexander Henry fore end in 7mm Mag. I shot it a lot with a 12X varmit scope and never got groups much better than 1 1/8" to 1 1/4" at one hundred yards. My rifle has a chamber that is on the large size at the back end to the extent that a fired case will not go into a Wilson neck die. 

I had a 45-70 that would not keep 5 shots on a 24" square target. I found that rifle had a .001" tight spot at the barrel band and a .0015" tight spot at the front sight barrel band. I sent that rifle back to Ruger and they put a new barrel on it for no charge and it shoots fine now.

The best I can suggest is to shoot it with your non-trigger hand under the fore end with the back of your hand on the rest. This way you will detect how heavy you are leaning on the butt with your face and it can stop some of the vertical stringing. At least it helped me a good bit with high recoil rifles.  Grasp the fore end with your forward hand and it will help reduce the recoil too.   

For bullets use flat base only if you are going to try lighter bullets. The light boat tails do not have much bearing surface and they have a longer jump to the rifling.

Powderhead, not in a #1 but in a small ring Mauser carbine just to give you some ideas, my best loads were 154 grain Hornadys with 46.5 grains of IMR4350 at 3.07" OAL; 160 grain Speers with 48.0 grains of 4831 at 3.20" OAL; and 170 grain Sierras with 46.5 grains of 4831 at 3.12" OAL.