Because you are essentially changing EVERYTHING about the ammo when you go from the factory loads to your handloads, I think it is premature to blame the powders you have tried with the 158 grain bullets.
First, I would suggest that you try some GOOD QUALITY 158 grain JACKETED bullets to be sure that you are not suffering from die adjustment problems, lead bullet to cylinder fit problems, etc.
If you can't get the 158 grain jacketed bullets to shoot about as accurately as the factory 125 grain loads, then I think that you need to address your die set-ups. But, you will need to check accuracy for a range of charge weights for each powder that you try, not just one or two.
If, on the other hand, the jacketed bullets shoot well, then I think you need to look into the aspects of the lead bullets that are related to their being exposed lead. There are many, probably starting with whether you have cleaned all of the copper fouling out of your revolver before you started shooting lead bullets. (I get the impression that you did not, given your pictures of single targets with holes from both types of bullets.) And, there are many other issues, to consider as well, which we can help you explore if and when they seem to be likely causes of your accuracy problem.