So pray tell, HOW do I contact these employer schools directly?????

No, Dear Boy, they won't tell you, they can't tell you; they dont even want to tell you, even if they could, because their main agenda is grumbling about China, having upset all their employers and every Chinaman they have come into contact with within China. The truth is, it's a hiding for nothing to attempt to avoid recruiters. Recruiters generally work very hard for their money-there's more in it than meets the eye.

Most schools just do not want to do all the groundwork themselves which the recruiters do. Just bung your details on sites and let the recruiters come to you. If a school rejects you, the recruiters tend to get the blame for it, when it's not their fault; how can it be, they won't get their dosh until you are placed at a school? At the end of the day, it is up to you to examine the contract and cross-examine the school when the recruiter eventually passes you over to them.

There are some exceptions of private schools , like Yuncheng IELTS, who do a lot of their own recruiting. Yuncheng IELTS (the headmaster is Mr River) have their classrooms outside of the school building at Middle schools. It's a good starter school for an FT-a flat with the job- a trained teaching assistant, one appointed for each FT, to see to all your needs, both jobwise and personal. Here is their link.
http://www.ycielts.com/en_index.php Good luck.