The school says you have nothing to worry about? If that is the case I would most certainly worry. In my experience Chinese English school owners are not the most, lets just use the word competent, bosses out there. Furthermore, that they have a cop in their pocket is not a sure thing, and even if this is the case, it's hard to know if said cop will really protect them, or just take their money and then turn them in. After all, if they bribed a cop, he knows their school is involved in illegal activity. That said, China has more cops then any other country I have ever seen. I suppose it's because the country is flush with cash, at least in part. If my home of America had as many cops as China does, I think things might be a lot safer. What you are seeing might simply be cops doing their normal everyday thing. People when they are doing something wrong tend to assume the worst, that may be what is happening here. You see more police in the area, you assume they are coming for you and your school, this could likely be the case.

It could also be the case that you are right, and that the school is about to be raided. The only thing I can say is, trust your instincts. If they really, truly tell you that the school is under surveillance, then my guess would be that and bribes paid to the cops have been more or less ineffective. If that's the case, and it sounds like it is, as cops bribed to leave the place alone would not be surveilling it, they are being paid not to after all. When people tell me not to worry when there is something to worry about, I worry.

The school also defaulted on getting you that Z visa. Having you go for the health check is a common ruse, they want to string you along, get you more committed, have you spend your own money, waste your own time. They never had any intention of getting your Z visa of course, they only wanted you to think that they would, in hopes that you would stay anyway. It worked, you are there.

My advice, and I can't guess at your education background, but if you have a college degree, and if you truly believe the school is being watched by the police, then I think you should leave, period. A school like that is not only going to break their word on other issues in the future, trust me on that, but if you are caught there working on an L, it's bye bye China. Taking this things into account, flight is best I think.

The only problem is, you only have an L visa. Most school will gladly hire someone who has the proper legal documents, it is very very easy to get a new Z for a new school if you already have one. It is very very hard to get a Z if you are in China right now, and only have an L. Many schools won't even want to talk to you if they find this out. If they had gotten you the proper documents, you'd have no problem, now, well you may, as in most places you have to leave the country to get a Z if you don't already have one. That means a trip to HK, and guess who will be paying for that. This is not the case everywhere of course, but it is in most places.

The Chinese are cracking down of late on illegal teachers, hence these kinds of laws. That L visa will make things very hard for you, and the school knows it. You are essentially their indentured servant now.

If you believe your instincts are right about the cops, then do leave, but secure a new job first if you feel you have time. If instead you feel a raid is imminent, then get the hell out of there as of yesterday.