Creating an Islamic Japan is impossible. Not ASB. Impossible. What makes me say that is that Japan is as far away from the Islamic heartland as you're going to get. This is not going to be a proper vanilla Islamicate society, any more than Indonesia is, because getting a vanilla Islamicate Japan involves the kind of invasion that would make Japan the most virulently anti-Islamic place on the planet.
Creating a Japanese Muslim culture is possible, but it's a project on par with Roman survival; it's possible, just barely, but it's going to butterfly away everything.
The first big question I have is where the Japanese Muslims would be turning to for advice. It's going to take time for Islam to become indigenous, and until that point their scholars and qaris are gonna have to come from somewhere. Where is that? Because whatever the answer is, it's going to have more contact with (and influence on) Japan than anybody IOTL did until the Meiji Restoration.
My other question is how Islam handles the transition to an indigenous Japanese religion. Once the initial iconoclasm is over, how much do Japanese mosques steal from shrine architecture, and how much is Mawlid just another matsuri? What demographics convert, and how does their conversion alter Japanese social dynamics?
I really want to see something like this done, because I love divergent Japans and want more of them in general. A Japanese Muslim society would be stranger than most fantasy settings, up there with Poland-Lithuania and Taiping China. The Mosque of the Silver Pavilion, built in Nagasaki with the pillage the wako brought back? I would trade my firstborn for a chance to see it.
And it makes me sad, because I don't know enough to make an attempt worth reading. Or anybody who does.