I was also able to register using a prepaid mastercard.

What currency does Smart-EX charge in? Amex foreign transaction fees are pretty high.

local currency JPY of course.

My Hilton Amex has no foreign transaction fees.

We used a German Mastercard to register on SmartEx last week and then successfully booked a train journey with Hayatoku 21 tickets for Shin Osaka to Tokyo, so it must accept some Mastercards.

I've tried a Mastercard and a Visa but neither is being accepted, for some reason. Amex, like many banks, has hidden charges for these transactions. Their conversion rates hide a loading fee and then they charge a few per cent for paying in a foreign currency. Wise is trying to make banks declare these charges in the UK at least.

If you want to book on SmartEx, you don't have much choice, do you?

Just buy tickets in Japan. Shinkansen tickets don't sell out in nonpeak seasons.

I had a similar problem. The only card I could get to work was my Monzo card. That got accepted straightaway and I have managed to book advance rate tickets for later this month.

You don't need AMEX. I use VISA. The problem comes from the credit card company having double security. I had this problem. Contact your card company and they will send you a link in which you give them "permission" for payments. At least, that's what my card company did last November.

I haven't had any problems once it was cleared.

If you have several cards, try them all. Maybe one will work.

Just FYI, here's everything you want to know about Shinkansen tickets. https://tokyocheapo.com/travel/where-to-buy-shinkansen-tickets-online-machines/