I've had two guns that double grouped. One shot great until one day it changed, the other double grouped right off the bat.
I eventually figured out the early offender(a new custom) with a scope swap. NF identified the problem as a lens bedding issue. They fixed it free, 2-day turnaround, no more double grouping. This is where it pays off to hold a reference scope(known good) in the safe.
The problem with the gun that changed from great to double grouping was very difficult to find.
It turned out the firing pin had started slipping under cocking piece set-screw.
The pin spring would push the pin to a forward location, and firing would intermittently move the pin to a second back location, where it occasionally stuck -until freeing up with further shooting.. The gun always fired ok, and both groupings were reasonably good(but not together).
Took 2mos to figure this out as there was no way to physically see the unknown cause, even with disassemble. I took many actions mentioned here & questioned/tested any stretch of recent changes,, no affect. Then one day I had a misfire. Within a few rounds, a second misfire. Now I knew for sure that I had a striking issue. I examined the hardened pin under magnification/angled lighting and found slight evidence of slipping under set-screw.
Now all I had to do was put the pin back where it should be and better secure it. Where should it be? Uh Oh...I didn't know for sure..
I had to do firing pin testing just like I do seating testing, and it turned out there was one setting that was better than all others. With this, it turned out a blessing, as I gained a solid 1/8moa over previous best performance. Locked it down, and the gun has shot fantastic ever since.
This is a Cooper M21 in 223.
I learned here that there is so much more to learn. That it's possible the abstract behind a gun favoring one primer over another -is firing pin setting, or spring, drag, trigger sear position, lube, temps, cocking piece, pin diameter, headspace,, anything affecting striking. That we can have any marginal combination of issues here that are not apparent, as every primer still fires, and their indentation is still fine. Those misfires I eventually had? Normal indentation!
Today I have a revolver that double groups due to a headspace issue with certain ammo. It always fires, but if I bring the gun from upward pointing down to target, -vs- downward pointing up to target, Jekyll and Hyde.
I've removed load density/powder shift from question by manually tweaking headspace from level. Same results. It's a delta in primer striking.