As I mentioned, I've been searching for additional options which would allow me to stay in Japan beyond my current visa expiration. Some interesting ideas that have been thrown my way:
Whether you're a tourist looking to extend his stay, a person on a one-year working visa, or even someone on a WHV (Working Holiday Visa - not valid for US citizens), this is a viable option. Establish a residence in a gaijin house, pick up a few part-time or contract jobs, and present proof of income (at least ¥250,000 I believe) to the local government office.
Japanese Language Schools
There are hundreds of summer programs from foreign universities offering intensive language study courses in addition to the private Japanese language schools. Depending on your citizenship, you may require a pre-college visa beyond three months of study; this would allow you to remain in Japan until your schoolwork is completed - you can even work part-time given enough time spent in the country and with special permission.
Some programs in Tokyo I've found that are still accepting applicants for their summer programs:
World Link Education
Some of the websites in which I've been searching for viable positions include:
Japan’s favourite cat breeds
1 day ago