Hmm, i like the idea that they may both be from Wano! My only issue with them being tied together is Shiryu was still a WG employee at Impel Down before being arrested. However that doesnt mean they couldnt have history before Shiryu went and became a jailer, since Issho wasnt technically an Admiral (and couldnt arrest Shiryu anyway).
I really like the idea of the final battles largely being tied to characters who have history with one another for sure, especially if they are more than standard 1v1's at first.
Scenery like this probably enough to make Fujitora blinded himself. Especially if the bodies are coming from both Shiryu and Fujitora's friends.
My headcanon thinks, both of them was coming and training in same dojo. The dojo had 2 Meitos, 1 that is held by Fujitora, he was probably Head of The Dojo. The other 1 was Raiu, which was locked because it was cursed, bloodthirsty sword.
Shiryu had his eyes on Raiu, similar way Teach had his eyes on Thatch's Yami Yami. When Fujitora was away, Shiryu massacred the whole dojo to steal the bloodthisty sword. Shiryu was already bloodthirsty even before he got Raiu. With Raiu, it amplifies his bloodthirsty even more.
Fujitora came back and saw the dead bodies. Something like this scene
Except of course more tame, because One Piece is shonen.
It all happened on night with heavy rain, thus birthed the epithet Shiryu of The Rain.
Might be the reason Fujitora wanted to disband the shichibukai. Man he hates the most was working for Government, but now a pirate. Shichibukai is basically also pirate working for Government, so Fuji doesn't want them around.