After more research we decided to reserve at the Marunouchi Hotel which is a stones throw from Tokyo station.
Cost JPY 38,000 for a nice corner room, but it's only for one night. Convenience was the main priority with such limited time. We can jump off the Shinkansen and checkin within ten minutes, then the following morning check out and jump on the N'Ex very easily.
Would be great if anyone has a Kyoto or Tokyo Kobe beef Steakhouse recommendation?
cheers