Why not just get a robot mower, and make the grassed area flat and square shaped, so it will mow it well. I am considering this option myself, between grass or fake grass.
What mowers are you looking at - I was unaware there were any reasonable options in NZ?
A house I looked at buying had a Husqvarna one installed. The grassed area was perfectly rectangular and flat, and they installed a boundary wire under the grass. Not sure how good they are or how reliable though. They aren't cheap though. But neither is fake grass I imagine. Would be interested in the pricing differences.