You don't need to leave the country to change visa status. I moved from tourist to humanities visa three years ago.
Most English schools require you to be a native speaker, but there are some that don't and the day care jobs usually aren't too picky either.
Sounds like this will be a massive downgrade in your lifestyle. Hope you're prepared for that.
If I was to give you a solid recommendation
David : save some money. Come to Japan on a student visa and go to a language school full-time. As a student you're allowed to work part-time so you can still work in a bar or whatever you want to do. Get n2 or n1 level jlpt. Then find a job in your current industry.