I vaguely recall reading something about how it was possible to sponsor yourself for a long-term visa under certain conditions, primarily that you deposited a large sum of money into a Japanese bank. This would show that you were capable of supporting yourself even without a job, and that your money in the bank could be seized if you skipped the country without paying your bills.
So does anyone know about self-sponsoring a visa? I might be able to swing that, it would sure make it easier looking for work, or even enable me to do freelance work (which otherwise would be impossible without a sponsor).