teacheraus is right. You can go down to the PSB on your own and ask for a tourist visa yourself. However, if you're leaving before your contract is finished you may have difficulty there. The PSB will ask why you're leaving early. Do you have proof that they've breached your contract in some way? Can you threaten them right back?
They're full of shit (no way does it take 2 weeks to cancel a visa) but if I understand your problem correctly, you need them to cooperate so that you can leave the school ahead of time and move on to a new school that does not treat you like shit. That means basically going along with their B.S. What solution do they propose to this problem? Or are they basically trying to strongarm you into staying?
Take blacklisting threats with a grain of salt. Yes a blacklist does seem to exist, but it also does not seem like any old school can just add anyone to it willy-nilly. They can probably make things difficult for you if you want to stay in the same province but that's usually as far as these things go, barring really extreme circumstances.