Upvote:4
(Qualifier: I am a Canadian citizen and Japanese permanent resident)
Japan does not have a non-working resident visa. All the working visa types require sponsorship from a Japanese company or a formal relationship with a resident. You are correct in that the long-term stay visa doesn't match your needs - that one is mainly for people who came here on a 1 or 3 year working visa, changed jobs a few times, have now been in the country for a decade and have enough freelance income to justify remaining.
Best you could do is an investor visa, but that will require a business plan, decent amount of cash, and hiring a few locals. A business plan based entirely on offshore work will almost certainly be rejected.
If both of you are under 25 you could apply for a working holiday - 1 year with rather vague working conditions. You won't actually have to work anywhere local.
Or (and this is quite common) get a job with the various language schools. Get a one-year working visa and quit on arrival. Your visa is valid until it expires, so you could set up shop in your apartment. Renewing a visa like this IS possible, you can show sufficient income and self-sponsor. No, it doesn't make much sense, but once you are here they are actually pretty good - last time I had to deal with immigration it took a whole two minutes and cost nothing.