I think this subject is a bit 'specialist' in that I would say approximately 99% of our members won't have had experience of the Turkish military service and, therefore, won't have a clue how it works with regard to immigrating.
I don't understand why you think London branch would be more likely to refuse you a visa on the grounds of your military service, but you don't think NZ will. You also say that you are allowed to go without doing your national service as long as you are living and working in another country. Wouldn't this be the case in NZ - you would be living and working there so there shouldn't be a problem?
I guess if you apply for a Visit Visa in Turkey and then go on to get a Work Permit in NZ, the officials in Turkey wouldn't see your departure as final because, as a tourist with a Visit Visa it implies that you will be returning. If you left Turkey with NZ residency in your passport, that would be a different matter I would think.
The reply from INZ is very non-committal and doesn't touch the subject of your query i.e. national service, so it's not very helpful in that respect. If you feel happier getting a Visit Visa and then doing the rest of your paperwork once you are in NZ, then go for it. If the Turkish military will come after you, I would think they will do it whether you apply in London or NZ.
Here's a
bit about Turkish miliary conscription if anyone wants to read up on it. Sounds a bit daunting to me.
