Hi 99whip, that's some good advice from the Captain, determine whether its you or the gun.
All the Pietta 1851s I own, right out of the box, will produce groups the size of your red dot. However, most BP revolvers group high.
Looking at your shot spread, it appears that you may be having an issue with trigger control. IMO don't worry about the load, 20gr, no filler, felt wad, and 0.375-0.380" ball should produce 2-3" groups @25yds from a rest. Once you are convinced that the revolver shoots accurately, practice will bring the rest home.
In the early 1970s I purchased a Colt Gold Cup .45 ACP 1911. The reason I bought it was to prove that I could shoot the pistol after being awful shooting the 1911 in the Navy. Since the Navy I learned to shoot revolvers accurately. I took the Colt to the range and began blasting away, but rarely hitting paper @25yds. I was becoming convinced that my Colt was a lemon. The guy in the stall next to me was shooting an accurized 1911 and was killing the center of his target. I told him that I was convinced that my 1911 was sick. He offered to test it for me. I gave him the pistol and two magazines filled with match wadcutters. He didn't take any time punching 14 rounds through the X-ring. He didn't say anything, but just handed my 1911 back to me and smiled. Since that experience, that 1911 has been my most accurate semiauto handgun. It just took practice, practice, and more practice.
Regards,
Richard