For those looking to purchase Shinkansen tickets in advance either for the Tokaido or Sanyo lines, there's an app called
smartEX. I believe you can reserve up to a month in advance. You can link the app to an IC card and not worry about paper tickets. However this option is only available for single tickets. One great thing about the app is that you can see the seat availability on dates of travel. This is great if you're going to travel on or around major holidays like New Year's. Currently, the app is only supported for citizens from the following countries: US, Australia, Singapore, Hong Kong, Malaysia, Thailand, and Taiwan