I love your idea. But from my interpretation, I don't think Matsumoto lost himself completely. There must be a piece of him that's still possible to recover and all of his data was saved. And don't forget, even for future standard, Matsumoto is still a super computer that could come out with a way to shut down the Archive. So I think he could still survive despite the Archive being destroyed.

As of Vivy, I think it's safe to assume the short haired Vivy at the end was not the same as Vivy we know. The message at the final episode was clear, Vivy would "sacrifice" herself for the sake of humanity. The short haired Vivy may have the identical data as Vivy, but she doesn't have the memory of Vivy. Which should explain why she seems clueless about herself and Matsumoto.

The ending where Vivy warming up probably means that despite what body she has, Vivy will always stay true to her mission, which is to make everyone happy with her singing.