Take the job only if you can get both 1/2 of the air fare allowance and 1/2 of the travel allowance after successfully completing the spring term. Apply through a visa agent or online in your homeland for a 90-day L visa - don't visit the Chinese visa office in person. No need for them to size you up there. Buy a return air ticket to China of the kind that allows you to change the date of your return leg out of China for a low penalty fee. It'll work out cheaper than buying a single to China and a single out of China. If things went pear-shaped visa-wise, you should still be able to renew your L visa within China locally, but for just another 30 days. Even so, that, along with the 90 days, will see you through to your school summer holidays.

The problem now is that the Chinese will soon amend their visa regulations, at the start of the new tax year and that might well get rid of some (or all) of the underhand ways that are adopted by Chinese employers to allow Westerners and other FTs to get long and renewed in-date visas of the wrong kind or Residence Permits that are for the wrong city/town for their FTs. I'm sure the head bummers in Beijing are well aware of most of the ways FTs have managed to get round the visa regulations with the help of dishonest school directors, recruiters and agents. So, beware. You needn't trust so-called gentleman's agreements in China, and bear in mind if the visa type is wrong, or the Residence Permit is invalidated due to where you are living and working, your contract is worthless.

Another thing to bear in mind here is that the new mandatory work accident and basic health insurance systems by which deductions will be made from an FT's salary might well impinge in a negative way on the ability of some Chinese employers to screw their country's visa regulations to benefit their FTs.

Finally, don't complain unless it's something serious. Keep your head down and avoid confrontstions. Realize that very basic accommodation is a possibility, but nonetheless you should be in accommodation that is rent-free and unshared, and better than your rookie Chinese colleagues.

I still think you're on a dodgy wicket, but I dunno for sure, you may come out of it well!