Wow, congratulations on the tag! I'd be hunting hard in Sept. in units 9 or on the east side of the state as Chris stated. If it were me, I'd take my bow and have a rifle as a backup. Also, as a native in AZ I know that I can find 370-380 bulls in most every decent unit. Even at that, I'd still be thinking of hiring a guide for myself for this once in a lifetime opportunity and not leave it to chance. NO, I'm not a guide or soliciting, but that's how I'd probably do it (and I live on a budget too). As a non-resident, I'd definitely recommend it. Your chances at harvesting a true trophy better, and I'd be asking for scouting pics, that way you can see the size of the bulls some of these guys are watching year round!
Either way, it will be an experience to remember forever, and we want to see pics of your hunt!