As far as I know,Foreign Experts' Certificates for foreigners intending to teach in the provinces can only be issued by the Provincial Education Bureau of each province,based in each provincial capital.
That would mean that FEC's for Sichuan province can emanate only from Chengdu,not Chongqing nor anywhere else in said province.The problem is that FEC's that used to be issued to foreigners who had no Bachelor's degree from the West are not issued any more by several Provincial Education Bureaus to such foreigners,in line with Beijing's policy on the issuance of FEC's.
In your neck of the woods,I'd expect that the goons at GAC/Owens School have got a 'special relationship' with the Provincial Education Bureau of Sichuan province that operates out of Chengdu.As you probably realize,no FEC means no Residents' Permit.And as you have rightly said,it's illegal to work in a province with an RP from another province.It seems that the goons at GAC/Owens School have no special relationship with the Provincial Education Bureau that issues FEC's for Guangdong province,based in the capital of said province,Shenzhen.
If I were in your shoes,I'd get out of Sichuan - it's likely that the GAC/Owens goons will use their special relationship with Sichuan Education Bureau,based in Chengdu,to ensure you cannot get an FEC for Sichuan province.Plenty of jobs elsewhere!