One thing that will help, in fact I would regard it as essential, is, no matter what your accuracy goal is for a longer range, move in close enough to the target that all or almost all shots are hitting paper. THEN you can see the complete pattern of your inaccuracy and work at tightening the group OR moving it to the point of aim, till you have done so to a sufficient extent. So long as you are dealing with ordinary terrestrial shooting in which wind isn't a major factor no matter if the dispersion of hits away from the point of aim is being caused by gun or shooter, decreasing range by half should decrease group size by half and bring it closer to point of aim by half, and conversely doubling range should roughly double the group size or distance from point of aim. Your "problem" could be as simple as you using a different sight picture as the "new shooter", or it could be a bezillion things combined. And if half isn't enough, make it a quarter, or whatever. Putting the muzzle against the paper is too close, but move as close as you need to... then... after you get it all figured out... back off from the target again. Another method to acheive the same result is to maintain the same range but increase the size of the paper target's area but that's usually less easy to do.

So long as you are missing "data" you are missing ability to interpret "data" and missing clues on what and how to adjust.

You can ignore the rest of this or not as you chose... but I never have and never will accept that dry firing has a useful and proper purpose. The fact that guns are now being made that cannot be decocked except by pulling the trigger is no validation, but rather just one more sign of the baleful influence of money over sense, cultural decline, and departure from what is righteous and holy. Materials now used hold up much better, but with a lot of older guns you risk breakage and in any case cause unproductive wear... plus adding some small element of additional risk... because to err is human, but to fail just one time to remember to clear the firearm, can be a downright catastrophe. I "heard" what was said about clearing... but I also know how often for whatever the cause, the refrain sounds, that "it wasn't loaded". When you dry fire you introduce another opportunity for human error, one I can altogether do without.