Hi. After living in China for 4 years I got a similar problem, I overstayed my Visa and they asked me to leave the country.
Many people told me don’t even try to go to Hong Kong to get the Z visa becouse they would deny it to me, but finally didn’t found any problem getting done the Z Visa in HK and after the resident permit in China.
I would advice you to contact with one or more agencies first of all explaining them your situation.
Cheer up!
