I think the cultural rationale is being overstated here. Let's be honest, even today New Zealand and Australia are about as similar as two different countries can be. Beyond those aspects of NZ's culture that are defined as 'not-Australia', there really is not much between us. The Maori certainly are a difference, though I doubt that other than for the Maori themselves that its much more than a symbolic one. How many Pakeha actually adopt Maori ways of thinking? I doubt very many. I can imagine its enormously annoying for some Kiwis to be patronised by Australians as the 'seventh state', but lets not overstate the differences. They of course were even smaller in the 1890's.
IMO it was the economic and security factors that were far more important to NZ's decision not to join the Commonwealth. In the 1890's Australia was a basket case, other than WA, while New Zealand was doing very well for itself. It made perfect sense for New Zealand to stay out of the federation in order to protect its economic interests at this time. Reverse this, and there are plenty of ways to have federation occur while the Australian colonies are prosperous and New Zealand struggling, and there'll be a much stronger argument for joining.
New Zealand also did not have to worry about its security at the time either. Australia itself was somewhat worried, as we know a united defence force for the continent was one of the main arguments, but there were no serious threats on the horizon. Britain was still very strong as well. If this were not the case, again plenty of ways to make it so, there would be a very good argument to include New Zealand in the federation. New Zealand would greatly enhance the defence force of the time, and in turn it would have access to much greater support than if it had to go it alone.
A century of two independent countries suggests that there are some fundamental differences between Australia and New Zealand that are unbridgeable, but this is an illusion IMO. We are more alike than Canada and the US, and if we'd been united from the start I seriously doubt there'd be a stronger New Zealand identity than there is Western Australian, or Queenslander. Sure, distance from the South-Eastern core is troublesome, but clearly not insurmountable.