If you can put a .22LR into a critter's ear standing broadside it should suffice. An Inuit woman killed the 1953? world record grizzly that way. It was trailing her, and she moved around some big rocks for the broadside shot; it worked!
Wowza...getting followed by a grizzly and carrying a 22...I would need a fresh pair of pants after that one!
But interesting you can hunt deer in Texas with 223/556. What's the smalls caliber allowed there?
I'll have to look at the regs…not sure anymore. Honestly, I think the regulations of northern states that don't allow it, are based on a) older projectile / powder technology coupled with b) older firearms / sight device designs. Archaic legislation at this point….for example, TSX bullet designs didn't used to exist…nor did the internet to help educate hunters.