Retirement tax questions

Are you sure the distribution is taxable by New York?  See this:

"The New York State Department of Taxation and Finance issued an advisory opinion explaining that a taxpayer’s payments from nonqualified deferred compensation plans to nonresident former employees, after termination of employment of the nonresidents, constitute retirement income and are therefore not subject to New York personal income tax, income tax withholding, or reporting."

https://www.stateandlocaltax.com/new-york/apples-and-oranges-new-york-applies-the-pension-source-law...

In any case, New York does prefer e-filing, but it permits paper filing of returns.  In fact, the instruction booklet for New York Form IT-203 contains mailing instructions and the following mailing addresses:

1. Mail your return by April 18, 2023.
   
   • If enclosing a payment (check or money order and Form IT-201-V), mail to:
     
     
     STATE PROCESSING CENTER
     PO BOX 15555
     ALBANY NY 12212-5555
     
     
   • If not enclosing a payment, mail to:
     
     
     STATE PROCESSING CENTER
     PO BOX 61000
     ALBANY NY 12261-0001

https://www.tax.ny.gov/forms/current-forms/it/it203i.htm#:~:text=The%20nonresident%20or%20part%2Dyea....