In the old days ( yes i know) before adhesives, if laying quarry tiles on a thickish bed we would use a semi dry mix that just forms the shape of your hand when squeezed of sharp sand and
cement, we would then put a thin slurry of neat
cement, on the surface of the screed and lay the quarries onto the screed, once a metre wide strip was laid we would then beat the surface of the quarries with a 6-8 inch length of 4x2 timber until they were all level.
if a thin bed of screed was required we would mix wet and the as knackered knees said sprinkle a neat layer of dry
cement to the screed , then lay the quarries and use the 4x2 again.
In answer to you dilemma i would suggest taking up the slate and using a suitable outside adhesive to relay on the remaining bed of sand and
cement as long as it is sound, as suggested by others