This is a very interesting theory, but I have an issue with it. If she had no physical body, why did Painter look like her when in her "world". Design said that Painter's body took her shape because she had enough Investiture to bend it to her Identity, and they deduced that this is the reason that her body didn't change for him, he wasn't Invested enough.
You could say he took the place of her cognitive shadow, but that makes no sense because her cognitive shadow was there, invisible to anyone but him.
The way I see this whole event, is that she had a body, held together by Investiture similar to a Returned, as we've seen the five scholars survive for hundreds of years on Investiture alone, also Hoid said she died when the machine started to work, so I think she actually Returned, making her a type II invested entity.
When she died, she would have reached the beyond, but hey body disintegrated since after all this time, when she left it, it couldn't hold itself. Think about it, the only Returned we've seen did is Lightsong, and we didn't hear him stretching out, we didn't see really see his death, we just know that he died, and we see his body after (which of course didn't disintegrate because it was only a few years since he died, not seventeen hundreds).
After that, like any highly Invested entity, she remained in the Cognitive realm for a short while. This is the time limit. If he didn't convince her to come back, she would continue. He obviously used his Connection and his art to dresser her closer, but pulling her, the original Yumi, back to the physical world, and convincing her to stay.
Hoid said she was as real as anyone else, because she decided. This means that she had agency, she could decide. She could have chosen to continue, but she decided to stay, using her Investiture to put her Identity into the Shroud and crying herself a new body from it, the same way she made Painter's body fit her Identity.
In the end, it was her, the same Yumi he was connected to, Identity and all, that decided to return.
What do you think?