I've just finished a very similar job in a local pub, nightmare to do but got good results.
Pre wet the floor apply scr leave to dwell, agitate, dwell, agitate, apply heavy duty tile and grout cleaner with some 220 honing powder, agitate, dwell , vac off, rinse, vac off, rinse, vac of then return the next day and repeat
That's what I had to do