When I spoke to a Maori lady at work before going to NZ, I mentioned my desire to try a hangi. Unfortunately it seemed it is more of a north island phenomenon. Ko Tane is a cultural village complete with performances and also advertise the restaurant food being cooked in a hangi.
I couldn't help feeling it is largely a tourist attraction for business purposes and the prices of the tour, the food and a photo for the show seemed as much.
The lamb shank from the hangi was in no way different or unique to another method.
Worth saying I've seen it but unless I experience the pit, I wouldn't pay for it again.