Question - would the course at NMIT in Nelson make you eligible for a student visa? See under
Offer of place here.
https://www.immigration.govt.nz/new-...-visa#criteria The institution itself would be able to advise you. I see from their website that it's possible to book a phonecall for advice.
About the work experience, see SM7.10 b here
https://www.immigration.govt.nz/opsmanual/#66799.htm, then SM7.10.10 and SM7.10.15 about being previously qualified. In your case, it would probably be a case to be argued over.
(By the way, I sympathize about the possible need to do the backwards step. When I was working, I twice had to put in time to get 'bits of paper' to prove skills I'd acquired by doing rather than on courses. It's bureaucracy wanting boxes ticked, and not enough, apparently, for someone to be able to SEE you successfully doing whatever it is.)