I understand the appeal to "hunt" these animals in the U.S., but you won't find me doing it. It's more a point-and-shoot scenario, than an actual hunt.
If I wanted a canned hunt, it would be pretty easy to "hunt a dingo" and just shoot my Australian Cattle Dog while he was sleeping.
There are actually wild, free roaming herds of Oryx in the southwest U.S. Don't recall the details of how or why, but I remember seeing a show on the OUtdoor channel a while back where guys were suing spot and stalk to hunt them in N.M. Supposedly they are pretty wary and hard to get close to.