I'm considering the same, as my Japanese fiance will be returning to Japan more-or-less permanently this week due to immigration issues and family obligations. I don't know much about the language agencies such as the ones you mentioned, but my fiance did tell me that there are businesses that hire "language coaches" on contract/freelance basis to teach English to employees, private citizens who want a tutor, and lots of independent little language schools that would consider a native-English-speaking person to be an instructor, though they would be picky about your credentials (university degree, TEFL/ESL certification). They don't want just a native speaker, since being able to communicate in one's native language doesn't always mean that he or she can teach it to others.
The majority of such potential employers are in cities -- large to medium size. Resort communities also are possible sources of work, particularly if they attract European and North American tourists. Rural villages and little towns are much more "provincial" and don't have as much need for English classes for adults (kids often get some English in school); consequently, you're more likely to find English-speaking Japanese people in the cities than in the hinterlands. That doesn't mean there aren't any possibilities there, just that they are less likely and much fewer.
The main issue, I think, is the visa. The big English-language "stables" help you get your visa once you sign on with them, but if you are an independent contractor it likely is not so easy. You'd need to be sponsored by an established business in order to get one. There is a visa specifically for teaching English, and the bearer can't do any other type of paid work while living in Japan.
If you speak some Japanese, it will help you even more if you do decide to try the less populated areas. You might be able to talk a village into learning English.
Don't know if this is helpful. But I'm doing research for my own possibilities and if I come up with anything that looks relevant, I'll forward it to you. My one advantage is that when my fiance and I marry (in Tokyo), I instantly qualify for a spousal visa that lets me do any kind of work I want in Japan. Well, providing it's not something illegal.