Private schools generally treat FTs as if they are a dime a dozen; that is, along with being easy to scam, they're also easy to find. Unfortunately, they're right.

Apart from what you've said above,I fully agree with what you have written.
As you well know,China is a country of many small cities.Teaching in one of them gives you much more job security and freedom in the classroom,simply because it's impossible for employers there to replace you timeously by seeking other FT's locally to teach your students by taking jobs on the side.So,even if you're not so popular for whatever reason(s),you'll be treated well;as the old adage goes - better to be a big fish in a small pond than a small fish in a big one.
But of course,in many of the less-developed places,foreign foods are either unavailable,or massively overpriced if they indeed are.Plus the night life there is probably much inferior to that of big cities.Also.you may find it hard to meet more than one or two other louwai,simply because there aren't any to be found locally.But that's not necessarily a bad thing!
I've taught at two private schools and four public schools in county seats,as well as private and public ones in big cities.Give me the small city everytime - your Chinese colleagues will likely be less picky and arrogant than their big city counterparts.And your students will probably behave well and be more inclined to study.

It's important for you to realize that if you are still in possession of your passport, it is probable that they have no intention of applying for your Z visa and plan on stringing you along as long as possible. In addition, it's doubtful that they are even a licensed school, so, if I were you, I wouldn't expect them to be applying for your work visa any time soon. This means: 1. You're working illegally. 2. You can probably leave without consequence because they've illegally hired you in the first place.

So, my advice is to take advantage of the fact that you have a place to stay when you move out of the apartment they've provided for you. Do not expect them to pay you what you're owed. Sever the relationship as quickly and cleanly as possible, but don't make any waves that could create a backlash for which you may not prepared. I assume you've still got plenty of time left on your tourist visa, so while you're staying with your friend search for a new job completely outside of Zhuhai. Don't accept employment from a private school unless you are absolutely sure they are licensed, and even then you must be very wary. Private schools generally treat FTs as if they are a dime a dozen; that is, along with being easy to scam, they're also easy to find. Unfortunately, they're right.