UPDATE: I have taken the laptop apart and taken a picture of the actual heatsink, it looks like this (green arrows show where there is some kind of connection). I did use compressed air to clean the space between the individual fins afterwards.
My reasoning is that all of the thermal conductance is achieved via those small dots where the heatpipes are connected to the other parts. As thermal conductivity relies on surface area, I was thinking about filling in the gaps to the side of the heatpipes. Hopefully, by doing so the heatsink is able to transfer heat more efficiently, leading to lower temperatures.
Thank you very much for any insights or hints! (and sorry for probably mixing several terms, like conductivity and conductance)
UPDATE: I have since taken apart the laptop and tried to fill the gaps with solder. Neither Indium (melts at ~ 156°C) nor regular solder would work, as both did harden as expected but could easily be pushed off with a Q-tip. My assumption was that some kind of material on top of the surface is causing the solder to not stick - however, even when using a metal brush with a electric drill, I was not able to make the solder stick (neither on the aluminum nor the copper part). This might be due to the inidividual parts not being heated to the melting point of the solder, but trying to heating them with the soldering iron did not even make a sensible difference. Additionally, I am too careful to heat the complete assembly up all the way to the melting point of solder, if I risk that the few existing connections might break while doing so.
In the end, I did sand down my CPU's IHS to make it even flatter and have accepted that this seems to be the limit that I can hope to achieve with this device.
Mixing some kind of adhesive / glue with thermally conductive particles might be an option but this was an avenue that I did not pursue further due to lack of experience with this process.