Clay, Arizona is one of those states that is not exactly non-resident friendly. I've experienced different results than your apparent first impression with Arizona. Don't get me wrong, it's a great place to hunt, but administratively it's tough on non-residents. By that I mean the fees required to antie-up and the draw odds. Closely watch your draw submission deadlines for Javelina. As I recall the deadline is October for the January hunt but check with AZ DFG. Those tags are no longer over the counter tags. If you don't draw consider contacting the several Indian reservations that reside within the state, as they offer hunts on their soveriegn lands also that are independent of any hunt opportunity the State of Arizona offers.
Hunting Javies are a lot of fun and well worth the effort. They are in constant motion