I have dealt with many people individuals who have overstayed. Most recently a Thai national  who  travel to RSA after changing his passport name (Fraudulently). Immigration picked this up and sent him back.
My suggestion is that you make inquiries to VFS Global who operate in both our countries.
In New Zealand they have offices in Auckland and Wellington.
Website https://www.vfsglobal.com/en/individuals/index.html.

Note: Our home affairs is terrible at responding to emails. I have personnel experience on dealing with them. This is also evident from numerous similar comments in this forum.!