I would like to add that as much as I am curious about figuring out exactly how everything works, I believe certain story endings/mechanisms are not to be overanaylzed. This can lead to us digging up potential plotholes/paradoxes, focusing on minor details, and missing the forest for the trees.
In this sense, I believe how exactly the script book title was changed is not important. What is important is that it symbolizes that through SXY's transmigration/experience/dream or whatever you wish to call it, she was able to successfully change the destiny of a supposedly prewritten character. Regarding the final reunion, (taking one out of Inception's book), it doesn't matter what world they are now in and how exactly everything happened. What matters is that, to them, their love was real, they can cherish the happiness in front of them, and they have fate in their own hands.