I believe you need to have specific NZ seismic experience to get CPEng, additionally you need a washington accord or equivalent degree.
They used to cross credit certain things, most notably from Australia you could just walk in the door and do nothing, but the seismic experience from these candidates was non existent in most cases. They have locked it down a lot more these days, everyone irrespective of prior experience needs to undergoe the same assessment.
Compared to US PE or something it doesn't even compare, i'd say it's a hell of a lot easier. It's not really a technical assessment of technical capability like I believe PE exams are. You put your best project portfolio forward for review. They have a 90% pass rate, so it's a bit of a joke as if there is a problem they just reduce the practice area description (the stuff you are capable of designing) until your set of skills meet the standard. Then this practice area is basically not made public and all CPEng are treated as being equal...
I'm really surprised you got away with your California stamp and just filling out forms. Certainly in the last say 5 years bigger councils have clamped down a bit. You used to be able to have anyone sign off PS1/PS2 without even having CPEng. Place I used to work had several people on the register at Auckland Council that were removed, leaving us with just one person in the office capable of doing it (only had 1 CPEng qualified person at the time in each office). Other councils are I gather much more lax than Auckland though, especially out of the main centers.
While Auckland can be a pain to deal with at times, I'm glad they do it having quite a bit of experience in peer reviews it's really needed, as the average state of structural design and internal verification processes is pretty poor.
I don't know if Christchurch still do it but they used to have what they termed 'performance' consenting, this as I understand it meant someone reviewed your first design, and if that went well others were not checked at all or had more minimal checks. Very dangerous ground in my opinion and no lessons seem to have been taken in from the recent Earthquakes and the lack of effective peer reviews possibly contributing the poor design of the structures that collapsed. Everyone makes mistakes, and you need processes to capture those mistakes on all work, not just one convenient job or project.
I'd get hold of engineering NZ and have a frank discussion with them. They'll give you whatever options are available to you. Also discuss options with the councils you deal with so there are no surprises. Failing that you could always partener up with a local firm.
Edit - there is no higher qualification (equivalent of SE), but there was some talk a few years back about creating what was termed a RSE (recognised structural engineer) that would require a exam on technical competency maybe similar to PE or IStructE exams. But this seems to have gone to ground.