If you need extreme accuracy and if a .22LR would work, AND all of the ammo you need is what you are carrying, then probably a primo rifle might be the Ruger 10/17. It's a 10/22mag (steel receiver) with a .17HMR barrel. The 99/17 would also be a good choice.
The .17 HMR rifles all have a rep for surgical accuracy and the .17HMR can blow a hole in a stop sign at 175 yards with ammo that doesn't weigh any more than .22LR. The report isn't much more than a .22LR and it has absolutely zero recoil. It's not uncommon to punch 3 holes in a target at 100 yards that can be covered with a dime.
So, you have a rifle that's surgically accurate, way more potent than a .22LR, and 1000+ rounds of ammo in your pack.