Goulds tags are crazy hard to get. Even for residents draw odds are in the low single digits. Things get way, way worse for NRs. There are only 70 or so Goulds tags, so best case, with the 10% NR cap, you have a chance at 7 of those. But, in reality you probably only have a chance at 2 of those tags. Normally the way that AZ works the 10% NR cap is that NRs are eligible for up to 10% of the tags for any particular hunt-- not total tags for that species. Since Goulds tags are mostly in the single digits for specific hunts, you can't get any of those tags. Last year there were only two hunts that had enough tags that a NR would have one tag available for the hunt. With sheep and bison it's a little different. NRs get up to 10% of total tags for the species, not by individual hunt, but I don't think that applies for Goulds. So, best case, you're in competition for seven or so tags, worst case, two.
Clear as mud? Put more simply-- if you want to hunt Goulds, go to Mexico.
With all of that said, if you already have the $160 license to apply for elk, deer, etc., it only costs $15 to apply for turkey. The application deadline for next years spring turkey hunts isn't until October, so you have plenty of time to decide.