To update my own post... after two separate unsuccessful support calls to TurboTax, I have decided to file my state tax aligned with my initial federal filing. Then, I will file an amended federal return, followed by an amended state return.
In the end, it clearly appears that TurboTax works in such a way that an amended state return is generated when an amended federal return is generated, so it was easier to just file four times rather than three.
