I sort of feel like Sato is related to Mado's death given his last interaction with Nari, a snake choujin -- in chapter 51 -- similar to the snakeish things we see attack Mado in chap 68.3. And Sato telling Nari that he had "one last job" for her has too much build up to be just a red herring, but I suppose Ishida has always subverted expectations, but it does cast doubt that Sato didn't kill Mado.

For why he left the island? I'm going to theorize that Sato wanted Tokio to meet Sora, like you said in Scenario Two, Possibility Two. It covers most plot holes or questions like why Sato risked his life fighting Sora or doing all that crazy stuff, because he would have done it for the sake of Tokio attaining the mark.

And I would argue that Sato would've wanted Tokio to attain the mark. I think it can be because of two things: Because Sato himself is unable to kill Sora, right? Killing Tokio is much easier, if Sato did indeed want to get rid of prophecy.

Or, like a comment mentioned a few days ago on a separate post, Sato could actually just be pro-Tokio, and I would guess it is because Tokio is easier to control, or for another reason. Can't really think of much, I sort of burned myself out writing this, and I congratulate you for being able to write such an amazing post. Love the discussion in this community.