Knauf Perlite as a leveling layer before insulation and screed

Hello everyone.
We have bought an old mining house and are now trying to turn it into our oasis of well-being through a complete renovation. This is relatively advanced and we are almost at the floor level. Unfortunately, old houses have the problem that the floors, walls, and everything are relatively uneven. The masons must have drunk more than they worked there.

Now to my problem. We want to lay underfloor heating everywhere. For this, we have torn out the old wooden floor that was on a concrete slab (structurally definitely sufficient and checked by a structural engineer). All partition walls are standing and the toilet is clad. Unfortunately, the floor sags about 6-7 cm in the middle. I would like to level this with a dry fill (Knauf Perlite). Then lay the tack boards for underfloor heating on top and then underfloor heating and screed on top of that.

Now my question is whether this actually works. Level with the Perlite and then insulation boards + underfloor heating + screed on top. I don't see a problem with that now. Just don't want any nasty surprises in the end.

Thank you very much in advance for your help.

Regards
Nitrox.

So I'm not really sure about the topic. If you have the filling inside and everything installed, where does the screed go then? Won't most of it run into the filling?? I also have a dry filling, but without FB. Dry screed was applied on mine and I think that's what perlite is meant for.

The screed cannot get into the loose fill. On top of that, there are the [Tackerplatten]. They are glued together with tape. At the edge, there are edge insulation strips whose foil is also glued to the [Tackerplatten]. So the screed will remain completely on the board.

Doesn't anyone here have a clue?

First of all, why is the floor sagging, and how can it still be considered structurally sound?
If it is sagging, something is wrong. Unevenness is okay or rather sometimes to be expected in old buildings.

A fill must be firm in its installed state, so not loose fill but a binding one, e.g., use Thermozell.
Underfloor heating on loose fill is also an absolutely bad idea because you cannot walk on it without leaving dents and footprints. The stability of the panels on loose fill is roughly like walking on a 2 mm glass plate lying on a mattress.
Even directly on PUR insulation panels intended for floor insulation, we did not lay our dry underfloor heating directly because it was too "wobbly" and prone to damage. Above that, we first laid 15 mm OSB panels across the whole surface. That is then also easy to walk on during construction. Then PE foil to make it waterproof.
So if it is really going to be the tack system, which I probably would not use in old buildings because of the weight (there will also be screed on top) and also because of the build-up height, I would definitely create a stable and firm subfloor (see Thermozell or similar) and first clarify why the floor is sagging.

By the way, we also had loose perlite as a leveling layer under cast asphalt screed, and removing the "cat litter" was hell. I would never put that in anywhere again.