I've shot many coyotes with the 223/53 V-Max. The majority under 200 yards. However, I killed a couple at 475 and 530. The problem with LR and the 223/5,56 beyond 500 is the need for a fast twist barrel and heavy bullets. I've used 69 SMK and 75gr A-Max out to 600 yds in competition. The A-Max works great. BUT, reading the wind is the key factor.
I now hunt with a 243 Ack Imp, with 85gr SMK and have made a number of kills in extremely windy conditions with great success. My best so far is 647 yds on a fox.
When I hunt locally in San Diego for deer I hunt with my 7-08 and carry both 120 V-Max and 154gr Hornardy SST. Killed a coyote at 815 yds with the SST and blew the living crap out of it. Impressive to say the least. Most shots on dogs has been under 400 yds using the 120s.
To each his own. With the 243AI/7-08 there is less margin for error.
Gonzo