So I found out it's actually possible to e-file the amended NY state return via TurboTax. Not even customer service knew this. But it requires being thorough during the amendment process to ensure you don't miss a crucial step: complete the subsection in the NY state return asking if the federal returns were amended. This also ensures form IT-201-X/IT-203-X is used and populated. It's easy to miss this step since you'd assume TurboTax would update that section automatically after amending the federal returns, and because other state returns (like NJ) don't require completing a special subsection like this in order to be registered as amended, plus TurboTax doesn't warn you if you've missed that step. Shortsighted on TurboTax's part and I've reported it as something to fix. I've now e-filed the amended NY return and mailed the amended federal and NJ returns.
