You have to use what you have at the time. Not to mention if I used my larger caliber I would have to explain noise to the police. 10 seconds more and no shot would have happened.
Note my Grandfather died from a .22 LR that hit a tree first.
I think people doubt the lethal nature of the 22LR and dismiss it as a simple squirrel gun. Close up they can do a great job at dispatching coyotes, but it seems all online forums want to dispute that and say it's impossible and they'll always run off. Your shooting proves that doesn't always happen if you know what you are doing, you can totally use what you have. Not my first choice on coyotes, but proof that it can do a great job of eliminating threats to your pets.
No doubt a .22LR is lethal, lots of people have been killed by them, check out Sgt. York. Even there are reports of at least two elephants killed by them. It took hours and many miles, but they did eventually die. That doesn't mean they are the perfect elephant gun or man stopper. They obviously will kill a coyote, but if you shoot many of them, you are going to find out it isn't ideal. My experience guiding lots of people on lots of animals, its better to have to big a gun than to small, every time and just because something worked perfectly once, doesn't mean it will work perfectly last time or the next 10 times.
If had my choice I would.use 25-20 and up. Shot placement is.more important than caliber. I am not an expert hunter of game, but almost always hit my target at any range. But I do shoot running deer matches every other month.