I skipped a little bit of the conversation.
your chrono speeds are not indicating an issue there that would contribute to vertical stringing.
something that might help is shrinking the pictures from the previous groups and placing them side by side with these groups so we can compare the progress.
as far as the riveting thing.
that's a possibility, the lead on the gas check would indicate that.
how to tell or work around that?
change the pressure timing, or top pressure under time.
maybe a diameter change.
I would be more inclined to investigate the stringing than anything else right now.
your just THAT,,,,,,,,,, far away from putting up some good groups.
scope mirage?
elbow pressure.
grip change.
neck tension/crimp.
all the groups over 1300 show the stringing, but if you take that stringing out you have rifle groups there.
I would start at neck tension and try again at the top load only and put more shots on paper.
maybe bump the bullet another .001 in diameter to help the tension out.
I don't know if you have been following me and Poppers conversation on the Cu/Zn alloy or not but there is some good information there on how an alloy reacts to pressure and might give you something to think about.