It is likely to be well worth investigating York City Archives. I can only speak from experience of the Essex Industrial School, where my GGF and his brother spent several years, but Essex Records Office have all the registers and many other documents for EIS. The admissions registers have been digitised and are accessible through Essex Archives on subscription. I had to order copies of the information in the discharge registers, as they have not been digitised, but they are a goldmine of information. The school kept in touch with the boys for several years after their discharges, and there are a lot of notes about their addresses, who they were living with, who they were working for and where, standards of dress, literacy and numeracy, return visits to the school, etc.
Hopefully you will find that York have something similar
