I suggest you question this knowledge Ilia.
The big question is =what exact kind of sand are you using? What size is it and where does it come from?
Hydraulic lime expands in water - it never cures in the sense you are saying, but you can see how this might be useful underwater or for brick mortar - not for fresco.
I currently have all the new books on Michelangelo for a sculpture project. I also have all the reference materials on the Mexican fresco artists. I also have the book on the Ajanta cave frescoes, and a lot of old plastering books.
This fresco material and technique you describe was rejected by Michelangelo - it dried too slow and there was effloresence - he used a lime putty (based on travertino) - and he added pozzolans (which are silicates) and brick dust. Vasari also recommends this technique. Michelangelo also differs in technique from you in that he does a lot of preparatory sketches and drawings - but he still created as he went along. As he went along, he first abandoned sinopia, by the time he got to the lunettes - he abandoned cartoons. And they also found a lot of secco areas from the hand of Michelangelo too.
Diego Rivera also used a dolomite lime putty, from the Mayan sources, washed mason's sand and imported french white cement. I have a video of him working - he too seems to work fairly freely. He did use fresco pigments, and probably brushes, imported from France.
So the two most famous works of fresco - the Sistine Chapel and the Rivera murals did not use the methods or materials you describe. It does not make your way wrong - but the point is there are so many ways - careful of falling into a trap. Making fresco seem like some lost, magical art, with exotic imported materials, and strange languages, only serves to drive people away - or back to their watercolors, acrylic and oils - or stuck in the mystique, rather than the art.
Also, involved in conservation as I am, no conservator in the world would allow a lime putty anywhere near their project without a chemical analysis.