Loose rings cause strings

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

Scope is loose, and you chased impacts, then used the wrong bore snake:cool: Far too many demons to give a single answer. Fix the scope issue and start again.

Obviously, the loose scope is most likely your main problem. Fix that problem first, then when you shoot again, be sure to let your barrel cool completely between shots. This will eliminate another likely issue, barrel heat. Then hopefully your problem will be solved. If not, I'd go back to the scope itself, replacing it with a known good scope. Good luck.

Also, check all screws, scope base, rings, and action screws, for tightness.

With the recoil of the cartridge your using, I'd Loctite the screws so the don't loosen up from recoil.

The ring screws all got the purple Locktite treatment, but the crossbolt has a spring washer of some sort. I don't know if that screwed with my FAT wrench when I torqued them initially, but I just went slightly ape with a crescent wrench before my next outing today.

The stringing hasn't really gone away. This time I had three shots in a tight 1"-ish cluster, the next two were three inches low, and the sixth was right back up with the first three.

Long shot but I wonder if crimping would give better consistency? Neck tension revisted at the least.

Possibly. I forgot to mention this was factory ammo, Federal Fusion 200s. I also had some American Eagle 185s, but I couldn't get any sort of groups from those, even with my POS Lead Sled.