I'm right here in Wyoming and chase them Wapiti's every year.
Peak of the rut is going to be sometime in the 3rd or 4th week of Sept.
When the Aspens are turning. Ruts can last into October, and Elk can have a "late rut" later in October, but the primary time known as the peak of the rut is 3rd week of sept.
I prefer the pre-rut myself. When the bulls are getting their voice. They haven't haremed up their cows yet. They are rubbing trees, wallowing, running each other off. And reacting more to your calls than during the rut. They are hard to get away from the harem when the rut is in full swing. But are eager to investigate that brush bull or cow call just before the peak.
Don't know where you are planning to go, but be prepared for any kind of weather! From t-shirt luches to 8" of snow. Very unprdictable weather in the Rockies in Sept.