I recently got a CZ 457 in 22lr. It is the sporter barrel/synthetic stock model.
It shoots pretty decent. I’ve tried a bunch of types of ammo and everything groups okay.
What I don’t understand is why I’m seeing a huge difference in POI between ammo brands. I’m seeing 3” shift at 50yds just from changing ammo. I normally see a POI shift but never that huge. On my other 22lr rifles I’d see maybe 1-1.5”.
Question is: Should I be looking at the stock or the barrel to fix this issue?
So far the info you have presented does not indicate any "issue" to "fix". You have not given us sufficient data to offer any opinions for trajectory differences. Primarily, you have not provided the ammo brand names and the muzzle velocities (V0) printed on the box, or V0 on spec sheets from their respective websites. The 3 inch variance in POI's between ammo brands is totally normal based on differences in V0 across many brands.
Note that the V0 listed in the brands spec's may not be the actual V0 of that lot of ammo. That number they list is an average of an average. Take with a big grain of salt. Eley is one of the few companies that lists the variance to be expected per brand. For example in Eley's subsonic line, Eley Team is listed at 1040 to 1085 fps, and Eley Sport is listed at 1000 to 1090 fps. That's a potentially big variance depending on what lot you ended up with. Add to that different bullet shapes, different lubes, different brass, etc, and it can account for alot of POI difference between ammo brands.
Comparing subsonic to supersonic would account for large POI differences, but I am guessing you are well aware of these and have separated these for testing? Its been a while since I shot supersonic ammo, but I recall it had significant POI shifts from the subsonics, not just in elevation, but also in windage.
If you could please list the various brands of ammo and their V0's that you aye are the big differences, then maybe folks here might be able to theorize about the magnitude of the group POI's.