You can't grind and re polish 10mm thick quartz tiles. I don't care who you are, and on that point New Image agree.
They didn't tell me they don't do work for a third party, they recommended that due to the nature of the product, the customer would be better off pulling it up and starting again, as even if they could grind and polish it it was unlikely they would be able to replicate the manufacturer finish. I agree with them, so does Marble Shine and so do any other professional floor re finishers that we deal with.
The OP stated there was £37,000 worth of quartz flooring to rectify. At £100 sq/m it's not unreasonable to arrive at 300+ sq/m.