How to make accurate cuts following spline

[college-courage]

Hi, I'm working on these abstract trees that need an accurate 6mm deep 16mm wide channel cut out for the LED track. I've tried doing edge-to-spline>sweep a rectangle>boole out approach, but sweep gets twisted around, of course, not following the normals of the tree. To make a rail spline would be super tedious, probably not accurate enough as well.. I've tried subdividing the spline but it limits the width to nearby edges, not giving me 16mm width.

Is there any other, more advanced techniques I could try? So stuck! Appreciate any help

See streenshots
https://drive.google.com/file/d/1_ed53qFViDkb1EXxmBwfgO4TTDIT0b4x/view?usp=drive_link
https://drive.google.com/file/d/1Pi7736P8iUNCrnRt-b7NsFFH1qE0sC9m/view?usp=drive_link

[Dr. Sassi]

Hi college-courage,

This is the Site Issue forum, which is used, e.g., when access to the Q&A forum is not possible. It is not a forum for anything else than problems with the Site.

Since this post will be moved to the Q&A forum, please use a new one to have the site admin check your access problems.

Please note that images don't provide a lot of information. Perhaps cut a section of the tree and copy/paste it into a new file. When it is below 1MB it can be shared in the Q&A forum as c4d file. (Larger files only via Dropbox, WeTransfer, Google, Apple, or Adobe cloud service, uploaded uncompressed, and the URL full pasted into the text. No HTML wrapper. Sorry for the long instructions, but safety first.)

All the best