Not reading that, before we get into anything Kizaru, Imma need you to first present how Law can possibly beat Katakuri. Tbh I don't have time to even dissect whatever you present, I'm just curious what you could possibly bring to the table.
Edit:
Just read the 2nd half, what relevance does island lvl mobility have here? Law's attack speed remains the same, the fact that Law can run away and come back doesn't solve any issues here, how is he landing anything? Law's attack speed =/= Shambles.
Law is already notorious for requiring tricks and distractions to land, that's his bread and butter, even in 1v1s. Katakuri hard counters anything offguard, Law can't catch him slipping, he sees whatever coming at him seconds ahead of time. Not to mention takt is also nerfed given Katakuri's logialike body. That's a recipe for disaster for Law.