I don’t know if you can, but I can’t really find anyone shooting a .22-250 out of an AR with much success if any at all.
Also, 55gr and 62gr is most common in 5.56. The military uses 1:7" twist barrels in 14.5-20" lengths usually for the round, and it stabilizes both bullet weights perfectly fine. If you don’t plan on shooting anything heavier than 62gr, then you’d probably be fine with a 1:9" or 1:8" twist. 1:7" is most common though, and you can shoot up to 75-80gr bullets with ease.
Serbu shotgun is classified as an AOW (Any Other Weapon), and to the best of my knowledge are illegal in NYS, like short barreled rifles and shotguns.