I've read your additional question. You don't need to wait for coming back to Japan as long as you leave Japan right before the expiring date, I think (plz, make sure by yourself). So theoretically it's possible like you go to Korea then go back to Japan on the same day. But it all depends on an immigration officer at the airport. If he feels suspicious of you, then your staying period would be shortened from the maximum 90 days. And it's almost impossible for you to stay in Japan after the period unlike in the US. There are thousands of cops to take on.
Comparing to us, you're lucky because a demand for English speakers itself exists in Japan. In my opinion, speaking Japanese skill is one of the key to grab opportunities. The ability shows us your passion for Japan.
Anyways, when you come to Tokyo, please let me know. I'll buy you some beer right before the expiring date. And I wanna ask you how it goes.