help with separating surface mesh

hello,

i have a surface mesh that looks like the following:

where there are the channels of the structure (channels in the axial direction) and connecting holes between them (the smalls holes on the right photo)

I would like to differentiate the channels by different regionIDs, my issue is that due to the small connecting holes, this is more complex task to do than it looks like:
without connecting holes i would do the following (that in theory should work):

  1. crop the geometry faces on each 6 planes using clip and keeping all the rest, to remove the faces on the planes

  2. use connectivity filter to generate the regions.

nevertheless, due to the connecting holes, almost all the channels are connected (one to another and the second to others etc etc…) and i finish with almost a single region for the complete thing.
i can not get my head around in how could i separate this data in different regions.
any input would be appreciated…

in case that someone wants to test here is the surface mesh data: FileSender