well i still dont know where i will stay during this winter, but i kinda liked the page of
Guest house Borderless-Tokyo Low cost accommodation all over Tokyo! because they seem also to host Japanese. I also got over this page
Reasonable Apartments Accommodations in Tokyo Kimi Information Center wich lists apartments for foreigners with less moving in cost and shorter contracts. Though the price is a bit higher you seem to pay around the same as for a single room in a gaijin house. Please be sure to check if you pay utilities seperat, as i dont know!
But it looks like the least you pay for moving in will be 1 month fee for the agency on that page.
Well after i had a look again on that page it seems to be more tricky than thought, but you may try your luck
