Do they? Vertical strings, I mean.

I was putting my new .338 Federal barrel through its paces on one of my Axises when I noticed a pattern in the groups: nice and tight horizontally but widely dispersed vertically. It was about an inch side-to-side but somewhere between four to six inches up-and-down at 100 yards (I kept chasing the impact, so I don't know for sure).

Everything seemed tight at the range, but when I was trying to pull the wrong size bore snake out of the bore I noticed the scope rings shifted forward and back on the rail. This was surprising because I had torqued the base screws with my Wheeler FAT wrench prior to shooting. It was also tight enough that my jiggle test at the range had not detected it, but it seems an obvious problem. I would like to know if it is the cause of the stringing. Unfortunately, since .338 Federal ammo appears to be rather rare around here, it will be a while before I can test the newly tightened rings.

Specs:
Savage Axis, .338 Federal 20" Apache barrel, some sorta brake.
Redfield Revolution 2-7x33mm, Primary Arms low tactical rings, Weaver 48347 rail
Federal Fusion 200gr