Peak of the rut around here is from the last week of September through about the 10th of October. I doubt if it varies much among the different western state that antlelope call home.

Also, you might consider a cow "decoy". We used one of these a couple of years back with pretty good success. I took a slide photo of a broadside cow; and then projected the photo onto a sheet of 1/4" plywood. Traced out the outline and all the features except legs. Cut out the legless cow with a jigsaw. Did a great paint job on one side - complete with a tail and an ear tag. Put two sets of handles on the unpainted side. Basically, you and a companion just slowly wander toward the antelope - right out in plain view - at an angle that puts you in bow range off to one side. Another guy I know did his cow decoy with the cow looking right at the camera - this was a one person unit.