Dont rely on the moon to tell you when to hunt. It is a factor to an extent, but in all honesty the rut is gonna change in every area every year due to many factors. Some areas bulls just don't talk at all during day, some places they stay silent due to wolves being present. It is about impossible to truly predict the "Best time". You can make an educated guess and go with it, and thats about as close as you will get. I have had elk in full rut during the beginning of september, then the following year in the same location the best action didn't come till first week of October. I have observed this both in Idaho and Wyoming. I personally would rather wait to the later section of September than earlier. Cows can come into a second estrus and I've had incredible rut hunting the third week of October. Each year changes and thats what keeps it interesting. If the area you are going is heavy wolf country, Which in Idaho is nearly everywhere unfortunately, Don't expect the bulls to be screaming all day, they usually shut up and go silent when the dogs are around. So in all that, to somewhat answer your question, I personally would wait to the last weeks of september to go, not the beginning. Much better chance that more bulls will be fired up than if you go earlier.