I just got a(n encouraging) response for the first time!
I had kind of given up hope of finding any work online, but today found a job teaching that really sounds great. It's in Kanagawa, the prefecture south of here - the prefecture where the sister city of Lawrence is, by the way. While not ideal, it's comfortably close to Tokyo - about an hour by train.
In any case, I really poured my heart into my cover letter, tried to make my self sound appealing while being honest to myself about my abilities.
Anyway, I just now received a response (it's 11 pm here) asking me to come see them next week some time. I wonder a little that they've responded, since they seem to need someone soon and it would take some time to process the application for a visa, but at least it's some hope. Finally, after nearly two months of searching, a bite!