the timing of the rut probably won't change much. however the time of day that the elk are active may vary considerably. A friend hunted in Id. a few years ago and the elk were silent in the morning and then starting getting fired up in the late afternoon and into the evenings, they called in elk but always in the afternoon / evening. Don't know if it had anything to do with the moon or not, just food for thought. If it were me I'd be out at both times of day trying to make something happen and hoping for the best. Good luck, sound like a fun hunt.