Second, of course you are a normal graduate. If it is too late to reassign, you can report to the Municipal Education Bureau first, and the Municipal Education Bureau will issue a certificate to the education in your district (or add a note to the registration card). You can also give feedback to the district education bureau.
Third, however, it is enough to have a local hukou and ID card, and you can recruit teachers. I wonder how the application conditions are stipulated there. By rights, you don't need a registration card. I suggest you consult the local personnel bureau or the Education Bureau for clarification. If this method doesn't work, you have to redistribute it.
Good luck!