Height adjustment on wooden gallery

Hi, we have installed a mezzanine in our living room. The base of the mezzanine consists of three-layer boards which rest directly on the beams.

Now, the thing is that we naturally need some lighting under the mezzanine and want to route the cables above the mezzanine floor so that the cables are not visible.
We are talking about some 5x1.5 NYM cables - so they add about 1cm in height.

Now we are wondering what we can use to level this out. In the end, laminate or cork flooring is to be installed.
Pouring material is actually not an option for me.

Are there boards that can be laid for this purpose?

Regards, Chris

The substructure of the gallery consists of three-layer panels

how about: "milling slots"? Such panels are usually at least 28mm thick. That would easily leave room for a 10mm thick cable (they aren't that thick, are they?). The cables typically only run a short distance and not from one wall to the other, so in my estimation, stability wouldn't be an issue.

It is about some 5x1.5 NYM cables - so they add about 1cm thickness.

rewire to a flat cable, that is then flatter and you don't have to groove as deep

how about: "milling slots"? such boards are usually at least 28mm thick. Then there would easily be room for a 10mm thick cable (aren't they that thick?)

That was also my first thought. But there are quite a few cables. Therefore I would prefer an alternative. At least it would be good if I possibly don't have to lay all the cables in the floor and for example only have to compensate half of them. The boards are 30mm thick

rewire to a flat cable, that is then flatter and you don’t have to groove as deep

Do you have a specific suggestion?
I have only found riser cables. But these are actually no longer used today or are not suitable for installation on wood