With that luggage, you could make good use of the excellent takyubin luggage forwarding service several times to avoid carrying more than your backpacks on the train. Just arrange with the front desk a day or two before you need to leave for your next hotel and it will be taken there and likely be waiting when you arrive. Keep enough clothes and personal items in the backpacks and send everything else ahead. Cost is reasonable and you may well never have to carry the big cases on the shinkansen. That is how most Japanese tourists travel.

The ticket enhancement you have read about is for the Nozomi/Mizuho trains on some main lines. Your Rail Pass will cover the somewhat less frequent Hikari trains over the same routes.