The Road to Redemption for Mukuro Rokudo

What would young Rokudo Mukuro do if he received memories from ten years in the future and learned that his future self had found redemption?

He transmigrates between worlds, enduring countless hardships as he searches for his redemption. (I don't even know who this redemption is myself.)

Pairing undecided. I don't even know what will happen later. This is my first time writing, so there may be some bugs. The story is told across different worlds, and Katekyo Hitman Reborn won't feature much at the beginning. The main focus is Bungo Stray Dogs!

Theme: Why is finding redemption so difficult?!