That's also my understanding. With an extra that Minchan is kind of a reincarnation of Seoho, but not a 1 to 1, but his own different self. And due to meddling of that crazy brother, Seoho got the chance to live in the new body in a new time but mentally as himself. He chose not to change anything, save any Bihwan, so that his past with Big an happens and also knowing that Bihwan will have love and happiness with MI chan. A very noble deed. Good for Minchan, bad for the crazy brother.

I may be tripping, but as I understand it, after what happened at the end of the first season, Seoho's entire soul appears in the room of nothingness, the place where it all begins. Seoho and Minchan have a strong connection that transcends time, especially in that room, where temporal boundaries cease to exist. That is to say, at that moment, the timelines of Seoho and Minchan become blurred. Jeoseung Samsin gives Seoho the opportunity to leave the room and start a new life, which I believe would lead to him inhabiting Minchan's body. But Seoho, instead of accepting it, uses it to get Bihwan out of the room, which is why when Minchan wakes up, it's still him.
In short, I think Jinmu's/Gwonryeom's plan failed cause Seoho choose Bihwan over been "reincarnated" in Minchan's body.