Change of Employer/Sponsor and Visa validity

Hello!

Recently I switches from a Working Holiday Visa to a Specialist in Humanities Visa through a Change of Status of Residency application for a teaching job. Since I'm not a native speaker of English I was quite happy to get this done at first.

The sponsoring organization is a language school employing only part time staff.
Now this is where it gets ugly. Basically everybody there is told they would get enough to live through their lesson based payment system. They write 200.000 Yen per month in the sponsoring section of the application. In reality after signing the contract, moving into their apartments and applying for the visa, nobody makes even close to that while being full time enslaved by this company.

They threaten to exterminate ones contract if I one doesn't take every lesson they assign even with just an hour of notice before actual lesson start which makes it impossible to do anything else including searching for better employment.

Now I have another school that would be willing to submit paperwork for immigration, but they only have one day of work for me. I would rather have them be my sponsor for the time being and the rest of the time free to search for work.

My question is the following: in case shit hits the fan and the threat of exterminating my contract comes true I would be without sponsoring organization. I know the visa is mine, but I'd have to be working within the next three months.
Would this work need to be full time or would part time work at an other school be enough to satisfy immigration at least until the visa needs to be renewed or I find something in full time?

Now I have another school that would be willing to submit paperwork for immigration, but they only have one day of work for me.

This sounds stragne for me, many employers ususally prefer employees who have already have a proper visa, even if they offer us full time position.

Anyway, I've heard that if we change employer (quit a job for the visa soponsor and get another job for non-visa sponsor), we apply Application For Certificate of Authorized Employment.

Maybe you had better ask an expert in order to get better answer.
http://ishijls.webnode.jp/english/syukastu/