Try some local bird sounds, they make a good alternate sound when the Dying Rabbit gets kind of tired. Being in N.M. I'd throw in some Bear Sounds. If Turkey sounds are legal in N. M. I'd try some of them as well. Javalina may be a good one as well. Are electronic calls legal for Elk and Mulie, just a thought. Electronic Calls are not just for Predators.
Here in Alaska I useThe usual predator calls, Coyote, Wolf, Dying Rabbit, Wood Pecker, Fox, Coyote fox wolf Pups, Bears, and Rodents. I used Moose Calls till they were banned. You want a rush? Climb a tree, then use the Black Bear call, especially the Baby Black Bear. Grizzly will come in fast, intending to kill something. The reason to be in a tree, luckily Grizzlies don't climb trees. Even when expecting it you will climb higher.