Soundproofing wooden beam ceiling (accessible only from below) + insulation

Good day,

who can give me a tip on improving soundproofing in a condominium?

Starting point:

[*]Old building, built around 1930
[*]Ceiling to the floor above: wooden beams
[*]On each side of the beams, there is battens
[*]On the battens lie formwork boards: two directly on the battens, with the next formwork board resting on these two, and so on
[*]From the lower edge of the formwork board to the lower edge of the beam: 9 cm clear height
[*]The battens will later be placed under the beams
[*]The floor above probably lies directly on without impact sound insulation
[*]The floor above is NOT accessible, as it belongs to the neighbor’s apartment
[*]All noises from the neighbor living above can be heard almost unfiltered
[*]Room height is tight, typical for old buildings; I do not want to "take away" more than the battens (3 cm * 5 cm)

I have thought of the following:

[*]Insulation with mineral wool between the beams. The battens create a stepped cavity... obviously not optimal, but cannot be changed
[*]A vapor barrier below the mineral wool
[*]Battens installed "loosely," i.e., with spring rails
[*]Plasterboard panels mounted to the battens
[*]“Floating contact” with the walls

The following questions:

[*]What else could I do to improve soundproofing?
[*]I want to combine thermal and sound insulation as optimally as possible

[*]I found soundproofing foam boards on the internet, for example used to insulate musicians' rehearsal rooms. Supposedly fire retardant, but is that a good idea? Such an installation could only be mounted over the entire area at the level of the battens

[*]The spring-mounted battens are supposed to contribute to soundproofing...

Who has a similar starting point and good experience with soundproofing? I am grateful for any advice.

Best regards Frank

The considerations are correct and in my opinion sufficient. Not much more can be achieved from below with simple means. I just don't see the point of the vapor barrier. If the floor above is heated, it would be superfluous. I don't think much of "miracle cures." Heavy films etc. are justified in exceptional cases, but for a "normal" ceiling perhaps a bit too much.

If you replace the mineral wool with wood fiber insulation boards, you can achieve significantly better soundproofing. The more mass, the better the soundproofing. However, these are somewhat worse in thermal insulation than mineral wool at the same thickness.