Well, Red Stag hunts over there tend to be around $5000 or $6000. You can pay a little more, and get a combination with a Bull Tahr and/or a Chamois hunt. However, if you want a better variety, cheaper price, and knowing that you like waterfowl like you do, I would look at Argentina for the Stag. They can start as low as $3000 for a hunt. Plus, they offer Axis and Fallow Deer, Blackbuck Antelope and European wild boar. I have always wanted to do an Argentina hunt.
As for plains game in Africa, it totally depends on country, length of time, number of harvested species, etc. I ggogled and found one 10 day package with 4 animals, for $5500 or so. found another that was also 4 animals, and it was a little lower in cost.
Of course, airfare and such adds to these hunts. If you are going to be in Africa studying the carnivores, I would just do it there. You're already over there, so why not. But, from here, my preference would be Argentina.
Well I guess I have to defend New Zealand a little. Prices for Stag hunts actually start around $3000, either for Free Range or Game Estate. You can do a 2x1 hunt for $3500 per hunter for 5 days including unlimited Wallaby shooting, and from May-August you can shoot Black Swan, Duck, geese, Native Pukeko which is also included. Airfares depending how far you book is around $1300-$1900, it is closer than both other countries with no snakes or spiders and is a not over populated. During the winter months you can ski, jet boat, bungy jump, and some of the best fresh water fishing in the world for trout and salmon. So I guess it really depends on what your after. I think if you have family especially New Zealand has it hands down for safety and price for touring around scenery no doubt. Asking hunters that have hunted in Both countries will give you a fairer opinion and will give your the merits and draw backs on both countries.
We also have fallow, wild boar, sika, sambar, rusa, whitetail, and game Estate Elk (8000acres) as well as the Tahr, Chamois, Alpine goat, Arapawa Ram. Australia is only 3 hrs away where we also hunt the Water Buffalo, Wild Ox, boar and tropical fishing to rival any country. I could go on!
The record books, that are put out by Boone & Crocket and Pope & Young and where I live is Henry Kelsey they are a great way to research a state or a province for big game. This does take some time but the knowledge it gives you, can be very valuable. Not all hunters have their trophies recorded, as where I live after the Hanson Buck became the new world record typical Whitetail, we saw a flood of hunters and now that has happened, some hunters are shying away from the record books but...