My .02 is not to go over labor day. #1 too early before the rut. #2 people and 4 wheelers. This is the last camping week of the year for the average summer camper.
Try to go the 3rd or 4th week.
If you do go and this is the only time you can go make sure you are ready to hike away from all the camping crowds. You will have to spot and stalk that early as bugling and cow calling will "Probably" be ineffective.