Sometimes, being reborn doesn't necessarily mean dying here, having your soul enter someone else's body, and then starting a life with cheat-like advantages.
Perhaps it's a life-changing event you'll never forget; perhaps it's a moment of sudden insight at work; or perhaps it's simply the loss of a loved one that makes you take a new look at yourself and completely change your life. Maybe that's what it truly means to be reborn from head to toe.
The most important part of a phoenix's rebirth should be a spiritual elevation, not merely a soul moving into a different body.
A young master from a feudal slave-owning family dreams of another version of himself in a different world. That world has a completely different worldview, outlook on life, and set of values from his own. The other version of him is righteous, kind, and brave, and slowly inspires him to change himself and alter the course of an era.
At times, he can even speak in his dreams with the version of himself in that distant world. These two selves, living in different times and places, influence and spur each other on.