RE: LONG range coyote gun
Not sure where you live, but I'm guessing that if you have large flat areas, you probably have a good bit of wind too. For that reason I would suggest a larger more powerful bullet/rifle combo so you won't have to worry about drift as much.
IMO, the .17, .22LR, .222, .223, and possibly the .204 just aren't suited to handle those longer shots under windy conditions...especially the .17.
I would seriously consider the .22-250 and .243.....although the .308 is another good option.
I know you already have a .243 that you can't group that far out there.....but if you are looking at buying another rifle, another .243 in the cabinet would allow you to save money by shooting the same bullets out of both.
Just an idea.