G'day paul, yep NZ is the only place you can take tahr, I have shot 4 Bulls since I have been here, have taken Chamois red and Sika aswell, although no real good trophies in the deer department, to be rectified in about 3 weeks
I would say NZ is among the best for red deer, particularly if you chase them on the South island around Otago, some big heads down that way. Worth having a look at Sika too - they are a unique deer and are like a mini version of Sambar, challenging buggers to hunt!!!
Advice wise I would go on times of year, obviously the roar is the best time to hunt any of the deer, for both Sika and reds late march to mid april is your best bet.
For Tahr, the winter coat is the best for a trophy, but hunting them in winter can be tough and requires specialist kit to get up to where they are. I took mine in November, thinner coats and the Tahr were high but far less ice to contend with. May is also a popular time for tahr hunting - their coats have developed but the conditions are generally still workable to hunt them in. I would recommend somewhere on the West Coast (South Island) as then you have a chance of securing Chamois and tahr in one hit.
Thanks for the advice on areas you made, namibia sounds good!!!