@user17597544422 , I think you path is correct to proceed.
As far as NY state goes -- you can paper-file with notation that you have filed for ITIN ( despite their "No writing" dictate ) OR just file after receiving the ITIN ( because any penalties etc. is generally based on amount owed). My personal pref. would be to paper-file and update later if needed. You can also call NYS tax office for suggestions explaining your situation.
Good Luck
