Hi Kiwis,
Just spoke with NZ Embassy in BKK. Call them and they will send a request form, when returned they will assess your situation then issue you with a letter for Immigration to extend past the 60 days. I know I know it completely depends on Thai immigration centre, what day it is and if the officer has had a good lunch or not but at least there is hope there.
TLDR : Answer Summary
A recent conversation with the New Zealand Embassy in Bangkok reveals that Kiwis can request a form to extend their stay in Thailand beyond the standard 60 days. After submitting the form, the embassy will assess the situation and issue a letter for Thai immigration. However, success may vary depending on the local immigration office's discretion.