Whilst in hiring a car I doubt it would ever be an issue hiring a car when you've been living here for more than a year, the risk is should you have an accident and they decide to check, you may find the insurance not valid, even if the other party is at fault. So best to send your license off.
There's nothing you can do about them retaining your NZ one when they issue you the UK license. They take it, and you will have to get a new one the next time you're in NZ.