The only way I could get Amazon JP to let me buy ebooks was to register a Japanese postage address on there - this was a while back though, and I switched to ebooksjapan as Amazon just wasn’t as easy to use (getting the kindle app to work on my phone is impossible!!)
I got the address from one of those postage services, where you register to be able to buy goods from Japan from places which don’t normally ship outside of Japan, and you pay postage fees to them whenever you buy something. Haven’t needed to actually use it for posting stuff yet, as since then everywhere I’ve needed to shop ships to the UK pretty reasonably!!