We have lithofin cement residue remover or the ltp grout residue remover as suggested by Paul would be my first test. Test two tiles first , get the dilution right ,iwould test 1-5 and move through in sections.
Also if you want to save time, as Julian said hire a wet vac ( if you dont have one) and this will save you half a day rinsing. You can rinse several times in minutes.