Have you considered stepping up to a .30 cal? The reason I ask is because a .308Win or a .30-06 are both excellent cartridges that would do exceptionally well on sheep out to 400 yards or more. And both have the advantage of being available with factory loaded FMJ bullets that would be well suited to coyotes if you want to preserve the pelts. And if you handload, the range of bullets available for .30cal is remarkable. You can get everything from light, explosive varmint bullets to heavy solids and everything in between. Ammo for a .308 or .30-06 is also readily available (not that .270Win or .243Win isn't) and relatively inexpensive.

Mike