I live in Arizona too, and i join East Coast games all the time. My ping to everyone is usually 150 or less.
I join Australian/NZ games too. My ping to them is usually 250 - 300.
Games in both cases usually run smoothly.
A 500 ping to the East Coast is not normal. Your connection must be sub-par for some reason, in which case you are absolutely right. You should restrict your games to the local area.
But, since most people don't have this issue, they (including me) will probably ignore your game name. Once in the lobby and I have a 500 ping to you, I will probably leave. Host launching with 500 ping showing is either not paying attention or not smart.
Your best bet is to host your own "Arizona" games and kick people with high ping. It may take longer to get a game started, but at least you'll have a good game.