Shinkansen ticket advice


Heading to Japan next week as a family of 5 (only one qualifies as a "child"). We will arrive and head straight to Kyoto on the Shinkansen. I'm looking into ticket prices and it seems like they have a family/group discount ( https://smart-ex.jp/en/product/ ) and discounts for round trip purchases.

What I am unsure about is that it seems like I would have to reserve a specific train time and since we will be arriving in the country that same day, it feels like a gamble.

Has anyone used these discounts? Are tickets reasonably easy to change if we miss our train? What would you suggest for a family of 5?

TY!

by ConsequenceNo8197