there's countless thousands of Eastern Europeans teaching English in universities in
China and then moonlighting in training centres on the backs of their legal residence
permits which enable them to have contracts with universities

There are many FTs from non-NES countries teaching in universities in China. Many are teaching Russian or other languages and many are illegally teaching English for the University and private schools. I know of two universities that have 'mislabeled' their English teachers in this manner. In the university, these teachers are at little risk but all teachers of English in 'training centers' that do not hold a residence permit and FES (now combined) 'tied' to that training center are subject to deportation. If detected, their university employers will be notified and their on-line government data notated. They are at risk of having their next residence permit application denied due to this notation in the Spring when they attempt to renew for the 2017-18 academic year.

The NES regulation has diminished the number of candidates available to teach in China, even for University positions. NES candidates applying directly to universities will have MANY offers; there is no need to use recruiters.

As to the oral English teaching capability of NES FTs versus FTs from non-NES, I do not see native oral language ability to be a substantial addition to a FTs skills in China. Chinglish is and will continue to be the international business language of China. Students that graduate university and acquire jobs at businesses where they speak English to Korean, Japanese and Philippine businessmen in China are well served by Chinglish. Their familiarity with British or American jargon is of no value.

An African with teaching credentials will likely do a better job teaching English to Chinese students than a U.S. citizen FT who graduated with a degree in economics, worked for two years at Starbucks who knows the meaning of twirking and barista but is unable to identify a gerund.