You can still have a successful elk hunt well after the peak of the rut
Many hunters plan their hunts around the moon phases. Some totally avoid hunting during a full moon, but I think this simply limits your time in the field—and hunting opportunities. Moon phases do indeed affect elk behaviour, but if you understand how, you can tweak your strategies accordingly. A full moon means plenty of light during the night, which increases elk activity, including breeding. To capitalize on this, you must hunt right up until shooting light ends, and be ready and waiting when legal light returns in the morning. Just keep in mind, this tactic often means many hours of walking in the dark.