Agree with the above. 9 people, including 5 kids, and "considerable" luggage in the green car of the shinkansen sounds like an unpleasant scenario - for everyone else. At least plan on using the luggage forwarding service from hotel to hotel to cut down on the quantity of dunnage you will be cramming into the very limited space behind the last row of seats on the train. That is how the Japanese travelers usually do it. The shinkansen rail cars are not even equipped with under-car baggage holds as you might find on Amtrak or some other rail services. The over-seat racks will accommodate moderate sized bags but larger ones will be a problem.

I also have to wonder if the 2+3 seating in the regular reserved cars might work better in this case than the 2+2 of the green car, which isn't really designed with larger families in mind.