You can't go wrong with the 22-250 AI. The 220 Swift is pretty equal in performance, but it's a longer case. You've probably got the short action?
I've got experience with both the swift and 22-250, the swift (mine anyway) was a little easier to find a tackdriving load for; but they are both tackdrivers for sure. The 22-250 is overall easier to load for, because I don't have to Full Length size and Trim/Chamfer/Deburr them as often.
If you are concerned with ricochets, stay with the relatively light "varmint" style bullets. You will loose some wind drift advantage, but you'll gain a longer PBR. The heavier/higher BC bullets would really shine in the 22-250AI, but they will also certainly ricochet more, especially if you miss the target. Alot of these high BC bullets in 22 are designed for "target" shooting only, some may not even expand on coyotes at 700 yds.?
If you learn your trajectories, and are good at reading wind...........the 22-250AI and the 22-243's, 22-6mm ect, will surely do the job on coyotes out at those distances. If your action is short, the 22-6mm may be too long (same situation with the Swift). I could never seat bullets out to the rifling with the swift if I wanted to use the magazine.
I've lost count of the number of coyotes and prarie dogs that I've taken with the 22-250/Swift cartridges.......HUNDREDS OF BOTH, with bullets no heavier than 60 grs (55's mostly). The farthest I've shot coyotes with them was around 500 yds, give or take a bit. The farthest prarie dogs were out around 700 yds. This isn't long range by alot of people's standards on this site, but considering the size of the targets and the expedient field shooting positions sometimes required (especially for coyotes), AND the light 22 caliber VERY LOW BC bullets.............these distances are long indeed.
North of 53
has made good suggestions on ranging equipment/hold over style reticles. Out to around 400 yds, we can "hold over" pretty well with a standard Duplex. Shots beyond the 1/4 mile mark benefit greatly by some type of ballistic reference in the scope (or Dialing it in). Dialing in range and drift can be more precise generally, but not nearly as quick. I really like the Nightforce Varmint Ranging Reticle with MOA reference bars/dots for coyotes, been using one since the early 90's.
Best of luck with your decision and your coyote hunting