heres a thought. say you are screeding over underfloor heating at 50mm rake 45mm of weber LAC over the floor. pump in weber 4320 quick drying screed to fill the agregate and form a solid floor. the screed would also wrap around the underfloor heating pipes. when its set lay 5mm of weber fineflo 5160 quick drying. i may have the part nos wrong.
anyway result is a liquid floor that is dry in about 2 days so you can lay ur tiles with no prep needed as its a cement based screed.
I have done this with 20mm chippings on a floor different thicknesses from 5mm to 40 mm. it went ok. the only down side was i layed it in december and it didnt set very quickly. was solid by 24 hrs though