Uh no.
I work for a flight school yes, but sending your logbook to a complete stranger is a not a good idea.
Apart from the fact stuff still gets lost in the mail.
The FSDO does not decide, the rules do:
Read 14 CFR 61.41, this allows flight training received form NON-US Instructors to be counted towards a certificate or rating.
14 CFR 61.41 - Flight training received from flight instructors not certificated by the FAA. - Code of Federal Regulations - Title 14: Aeronautics and Space - Subpart A: General - Id 19563103 - vLex
Read 14 CFR 61.51 this requires you what to log
FAR Part § 61.51: Pilot logbooks -- FAA FARS, 14 CFR
You need to start the proces of validating your NZ PPL as this can take up to 60 days. You will be send a letter of verification by the FAA which is valid for 6 months.
Which means you need to complete your CPL training within 6 months or apply for a new letter while you are in the USA.
If it helps, send me a scanned copy of your documents and logbook pages and I will take a look.
I'll PM the email adress.