I wouldn't recommend going for just a turkey.
That being said, it is a wonderful hunting destination and the scenery is second to none. It is a wife friendly hunt and I would highly recommend that you take her with you.
If I were to go again, I would want to hunt tahr and chamois again. That was two of the most challenging hunts that I have been involved with. The turkeys are a piece of cake. I didn't shoot one but it wouldn't have been a problem. There probably isn't a limit of the number of birds that you could take in a weeks time. New Zealand has no game laws, limits, or seasons.
I am unsure of the cost for a trophy fee but it wouldn't be much. If you included a couple of turkeys into a tahr/chamois/red deer hunt, it could cost up to $10,000 for a 7 day trip. It just depends on what you would want to hunt. You could go for a 5 day hunt and hunt one animal for around $4500 for the two of you and add a few turkeys to that hunt.
Airfare to get there would be around $2000 or so per person.
Let me know when you want to go.