RE: how do you guy do it
Sight in/load development I use a bench and sandbags. Like said I know where to place the blame if I miss. I also practice from various field positions so I havehandle on my real life ability.
I have tried many rests over the years some are better than others but I find sand bags to be the best for my situation. I make mine out of old jean or coverall's legs by just adding sand and tie off the openings, this way I can stack them and mold them for different guns/shooting styles. I make sure to place sand bags on thefront & rear of the stock to ensure the gun is solid...this eliminates the rocking when breathing.
To me sounds like you might be flinching a bit at the trigger pull or something with mechanics. Maybe in antcipation of the recoil, muzzle blast, could be yanking the trigger or a bit of target panick where you try to control the bobbing crosshairs and actually worsen the POI. Make yourself some sand bags, this way you can just concentrate on the mechanics of shooting. Practice will improve your groups...trust me! I was never a good paper shooter but after range time and finding aids that helped make it more enjoyable I have greatly improved and really enjoy going to shoot paper now.
BTW might be good to ask a experienced shooter to watch you shoot and possibly point out what you may need to work on. Even a buddy who concentrates on watching just you can give you some clues.
Best of luck & keep practicing!!!!!!!!