INZ timings are elastic - they're based on averages, and can't be taken as a promise. ALL applications have their evidence thoroughly checked out, and if someone doesn't reply to a CO's query, it can cause delays, so everyone has to accept, it takes as long as it takes.
As it says on the second and third threads I linked to above, although the regulations say the Australian partner should be established in NZ, when that poster explained his situation to INZ, they allowed his foreign partner to put in for partner-sponsored Residence straight away, before arriving in NZ. So that's something you might want to check out for yourselves.
It is certainly possible to have two kinds of application in simultaneously, and the evidence doesn't have to be duplicated if it's recent enough. Check on the INZ website about police certificates and medicals for details.