What will you be applying for at immigration? Will you be applying for a non-o visa or a extension of stay or both.
Proof the 800k baht came from abroad is only needed to apply for a non-o visa. Immigration requires proof it came from abroad by way of a transfer into a Thai bank.
If you already have a bank account you should transfer the 800k baht into it.
You can have a cashiers check sent to Bangkok Bank in New York and have it credited to your account.
See: https://www.bangkokbank.com/en/Personal/Other-Services/Transfers/Transferring-Into-Thailand/Foreign-Remittance
If you have a Bangkok Bank account it is also possible to transfer funds into it via the New York branch but it has to be in the IAT format for ACH transfers. See: https://www.bangkokbank.com/en/Personal/Other-Services/Transfers/Transferring-Into-Thailand/Transfer-money-from-US-to-Thailand-via-Bangkok-Bank-NewYork-branch