I love pre-rut/rut, I think if you wait to hunt them in full rut you'll hear them, but you won't be able to get them away from cows...but on the other hand you want them bugling too. I would think it would be mid Sept would be ideal time to chase them.

try googling "idaho elk peak rut" sometimes outfitters in areas will show their book dates etc...for peak rut dates, or just someone else online will post the dates...

best of luck!