Why not just bring your bag with you on the shinkansen? I just got back from a shinkansen-heavy trip (green car JR pass), with a large checked, smaller carryon, and a backpack. On the Hikari and Sakura green cars both ways, I was able to get either a baggage seat or a luggage storage area seat in all directions and when someone who didn't book one of the luggage seats and had their bags stored behind, the conductor made them move their bags. That said the overhead luggage area on the N700S is pretty large, saw several full size checked stored above with no problem.