From my experience travelling in Japan, online booking is a mess. But every time, the solution was simply to go to the station, walk to the counter and ask. The guy will get you exactly what you need, may give you alternatives if what you want is unavailable, tell you about unusual connections, take into account whether you prefer to be seated together or if you prefer to leave ASAP. This is real service from competent tellers. And I am saying this as a tourist who practically can't speak Japanese. And for paying, cash always works. Alternatively, if you don't need to talk to someone, there are also some ticket machines that are rather well designed.
It turned out to be a better experience than in most other places that may have better websites and more digital payment options. Yes, you have to physically go to the counter, but the is a good chance you are going to be in train stations a lot, it is not really a problem.
It is millions of time better than some booking websites that are designed to extract as much money as they can from you instead of helping you (ex: low cost airlines). No, I don't want insurance, no I don't want extra luggage, no I won't pay extra to choose my seat, no I don't want priority boarding, no I don't want to rent a car, no I don't want a hotel, no I don't want your app, no I don't want to subscribe to your mailing list, yes, I know what I am not getting, don't try to upsell me a second time, I just want a ticket to my destination!