I can't answer regarding police certificates as I have no experience with this, but as for filtering, it only applies if you have one single conviction.
If you have more than one separate conviction, then I'm afraid none of them will be filtered - even if all of them would filterable if they were sole convictions.
Hopefully with the huge amount of time that has passed and the fact that they are not massively serious convictions, it might be OK for your visa, who knows, though of course that's up to the Kiwis. Oddly enough, did you know New Zealand is only country on earth where car insurance is not mandatory. So driving without insurance is not a criminal offence in NZ!
Good luck with the visa and the job.