Hey Benj, congrats on your tag. I couldn't believe it when your dad told me you drew in the random draw!
So your season is August 27 through September 25. The moon is full on the 17th (end of the third week and beginning of the fourth week). I would even consider the second week, Sept 3 through Sept 11 but that is a tiny bit early. Ideally I would go somewhere around the 10th to the 20th if it weren't for the full moon. The best time would be prerut, immediately before the rut I would think. Your bigger bulls haven't herded up yet but are thinking about it. Typically they are going to be easier to hunt before they are herded up. If it was me, I'd likely go the second and third weeks (Sept 3 through Sept 18) if you can take the time off. As the moon moves closer to full, make your hunts earlier (start a couple hours before daylight) and try to locate and get close to bulls before daylight.