You'll need an ADIT stamp, but I agree, by Wednesday isn't likely. They're usually mailed, my daughter's came pretty quickly after she lost her green card, but not that quickly. https://www.uscis.gov/i-9-central/form-i-9-related-news/temporary-status-documentation-for-lawful-permanent-residents-lpr
But you don't need the GC to leave the country, only to re-enter. So I'd suggest you phone for the ADIT stamp and then when it arrives ask somebody to courier it to you in NZ?
I'm sorry to hear of your situation, and hope you can find the GC's.