A STAG is absolutely not a New Zealand EGOT. The point of the EGOT is you’re award-winning across multiple genre. A STAG means you’re award-winning across music.

A real NZ EGOT would be something like a NZ Screen Award in both TV and film categories, an Aotearoa Music Award, and I guess a regional theatre award, or maybe even take a slightly different tack and use a NZ Comedy Trust Award.