I think the word "sponsor" scares off the HR department. I'm able to pay all the fees, I just need the company's name (and a commitment to stay in the role for at least a year if I remember right).

You have to understand that it’s not as simple as that for the company.

In order to sponsor your visa they have to demonstrate that they attempted to hire New Zealanders for the role and there was nobody suitable for the role.

That means being able to supply proof that you made a reasonable effort to advertise for the role, and giving lists of NZ candidates who applied but where not suitable because they lacked the technical requirements for the role.