A:You're measuring from the wrong corner ...! English teaching working experience means a squat!  Nobody is saying (... or even doubting ...), you aren't a good English teacher!It is the 'Law-of-the-Land', which prevents legal employment of non-native English teachers in China.
You could never obtain Working permit in China as a non-English native passport holder since June 2017, with or without School's quanxi, unless you hold BA completed in a native English country.Native English passport requirement at English teaching jobs is the same everywhere around the world.China, Russia, Armenia, Turkey, Spain, Portugal ..., where I've tried, ... and at the last two countries, I don't need too many permits, 'cause I hold EU passport. i.e. I could literally start legally working in the classroom few hours after the initial interview.   '... just get another profession ...' is the only 'short-cut' available!  https://www.grammar.com/a-vs-an-when-to-use ... let-me- 'P.S.' - you ... Non-English native teachers should look from a different perspective ...  'How would you fancy non-native teacher of Farsi, originally from Madagascar or Botswana?'    ROTF  &  LM-b-AO  i.e. 'rolling-on-the-floor' & 'laughing-me-Botswanian-arse-off' -- icnif77