Even if one were to leave it at the current 6cm, I see no problems there. It is usually said that the coverage (with screed) of the underfloor heating pipes should be 45mm, while for the pipes themselves 20mm is calculated (mostly 16mm/17mm pipe with carrier plate underneath). This results in a "standard height" of 65mm for a heated screed.
Depending on the screed composition, however, only 35mm coverage is possible to my knowledge.
In this case, one probably cannot use stapler plates because these as a carrier layer usually require at least 20mm of insulation (the stapler needle has to hold in something). Instead, one uses, for example, studded plates without insulation or possibly a hook-and-loop system and attaches the necessary insulation layer from below on the basement ceiling.
The controlled residential ventilation can also be accommodated elsewhere; it does not necessarily have to be integrated into the floor structure (I am personally not enthusiastic about this anyway because it often requires very small cross-sections with unfavorable pipe dimensions (oval instead of round)).
Another option would naturally be to simply build the floor higher. The problem areas "stairs," "doors," and "windows" have already been mentioned. If I remember correctly, you wanted to completely replace the windows anyway; so that would not be a problem. Possibly, there may be an insufficient sill height of the non-floor-to-ceiling windows (in Hesse, I believe, 80cm is required). Basically, however, it is no big deal to add another row of bricks to the window.
Raising the lintel for the doors is also no rocket science and maybe even desired anyway (2.11m instead of 1.985m).
With the stairs, one would have to look – according to DIN one may deviate up to 15mm from the rise at the entry/exit step. Alternatively, one could work with so-called "renovation steps" (possibly wanted for aesthetic reasons anyway?) and evenly distribute the additionally required build-up height onto the steps.