At the end of August, JR announced beginning May 2020, they will be implementing new luggage restrictions on the Shinkansen. The restrictions are being applied to the Tokaido, Sanyo and Kyushu Shinkansen. This will include all Shinkansen between Tokyo and Kagoshima. We do not have all of the details as of yet, but here is what has been announced.
Luggage with a combined height of 160 cm (63 inches) or less
These suitcases will not be subject to any restrictions. However, these items will have to be stored either in the overhead above your seat or on the floor in front of you.
Luggage with a combined height, width and depth or 160 cm to 250 cm (98.5 inches)
These suitecases will require a reservation for storage of the luggage. The reservation can be made when you obtain the ticket. You will be assigned a specific storage space, and will be given a secret code to access the storage space. The storage space will somehow be indicated on your ticket. If you do not have a reservation for the luggage between 160 to 250 cm, you will be charged a 1,000 Yen fee per suitcase. People in the last row of seats at the rear of the car will store their luggage in the space immediately behind the seats.