Moving to Tokyo with kids, how does enrolling in school work mid-year and mid-move/location

Hi all

Tried to do a bunch of searching for this but couldn't quite find an answer. If it's been asked before, please link me!

TLDR: We're moving to Tokyo area from the US in a few months with a 4 and 7 year old. We want to have them at the local public school, but:

1. do schools allow mid-year enrollments, or do we have to wait until the next school year (April)?
2. what do we do when we're in temporary housing (1-2 months immediately after landing) vs permanent (ongoing rental) if they are in different areas? Can we enroll in a school in our target neighborhood, even if we don't currently live there?

As I understand it, we can't rent anything from here, and can only start looking and renting after we land since we'll need our resident/zairyu card in order to do so. So we'll likely be in a longer term rental for 1-2 months (eg AirBnB or furnished apts) while we're apartment hunting.

Making this up, say we get a furnished apartment in Shinbashi, but want to end up renting in Kawadacho.

1. Can we enroll our child in a Kawadacho school even though we're temporarily in Shinbashi? or
2. Do we need to wait until we secure more permanent housing to enroll?
3. Do we need to enroll in the Shinbashi school since that's where our temporary rental is, then switch to a school once we find a place in Kawadacho?
4. Something else?

ありがとうございます！