I have had many opportunities to shoot a bobcat...sometimes even had two within shooting distance but never have actually shot one. I was always waiting on that big buck and didn't want to shoot and scare him off.
I did trap with a guy one year and we caught one though...along with a bunch of possums, coons, and dogs...including our own about 2.5 miles from the house. They are beautiful creatures.
Yes, we can sell a good coyote for $40 on the hoof. Yet my primary mission is to make them dead, and I like when they become dead right there on the spot. Track jobs take up time, not to mention aren't as fun to watch on the subsequent video. The 22-243 is like a lightning strike most of the time. Travis was running a 22 Creedmoor for the latter part of last year and had fantastic success as well.
Lots of ways to kill coyotes, but up here a .223 just doesn't have the mustard to really get it done well. A guy can't always put the round exactly where it's suppose to go, and the fast 22 cal's buy us a little forgiveness.
Jekyl, I think the 6.5Grendel is a great little cartridge. I would see you having a lot of fun with it! Yet when it comes to AR's, there is a certain utility in being able to have that much 5.56 ammo laying around. A guy has to get pretty specific regarding your requirements before I could really narrow it down. Lets not forget there are a TON of other really cool rounds you can shoot in an AR. Heck, a 204 ruger makes a pretty great little coyote round. Much better than a .223.
Personally, if I were in your position I'd simply buy 2 rifles. I'd buy the AR you want, in 5.56, setup just how you want it. Then I'd call @tscustoms and get him started on a custom bolt gun built out how I wanted it. :)