Contour minimal surface connections wood joinery cnc

Hello community
I am trying to connect extruded contour slices with wood joinery to send them to a cnc for digital fabrication. The shape is Batwing minimal surface
The thing i am trying to do is first eliminating each second layer so i can insert the wood joinery between the first and third layer


so basically making a hole between the intersection of first and third layer
I am not sure if i did the script the most efficient way but it was a result of a lot of experimenting
The joinery looks like this so

basically it holds each 3 layers (2 layers with an empty space for a layer in between.
As you can see in my script i just made it do this for separate 3 layers so my question is how to do this for the whole geometry the each 3 layers are connected together. I have been making a lot of thinking and experimenting but i didn’t found any solution so i would be really really thankful for any help!
Here is a file with the geometry before and after slicing (Obviously i didn’t make it to contour the Mesh in grasshopper and sort the list so that the layers with the same z are in a data tree so i just did it in rhino).
Here are my attempts in grasshopper to join each 3 layers together .

Similar project ti what i am trying to achieve


Another way of making this could be to divide the surface of the intersection layer but also this didn’t work for me because it doesn’t position the Jointing element in a proper right position (like near to the edges and fully random position that has nothing to do with the surface)
Thanks for your time !!!
schichtverbindung.gh (23.5 KB)
Target Modellayers.3dm (10.3 MB)

Hello
Not on my pc now, if it could help, similar question was asked on old grasshopper forum with the similar photos as above.
Script named
WoodDisplay_ID_with support_v2.gh
Boot support V2 for V5.gh

Could you internalise the starting brep(s) - or indicate what in the model you posted it/they should be set to? Hard to follow without a starting point…

I found the discussion

And for the record First images are

Custore Pavilion / Anna Dobek + Mateusz Wojcicki