Hi Rob,
I would just start with Google Maps to get the route (including transfers etc) and then use the following website to see if scooters are ok or not.
https://www.ecomo-rakuraku.jp/en
You can enter in a station name and in the details there is a section called “Movement information in handle type electric wheelchair” (which is what they call scooters). It says the answer in Japanese (I guess they made images instead of text) but if it is a circle, you can use your scooter there. If you get an “X”, then you would maybe need to adjust your route to avoid that station.
As for requesting help from JR, if it is just a local line or a train without reserved seating, you can just show up at the station and tell them where you want to go and they will assist you (though you might need to wait a bit). If it is a train with reserved seating (like the Shinkansen or Odakyu’s Romance Car etc) then you will need to to go in advance and book your tickets. How far in advance depends on the train line, etc. But reserving accessible seating on the shinkansen can take up to an hour, so I wouldn’t recommend going the day-of.
Hope this helps!