Ack, it’s worse still! You can’t use Braet#1 for both the front and back boards if you want to cut them at different heights! Likewise, you can’t use instances of Lige Braet for the middle three boards! Because they end up cut at different places, they all need to be unique components or groups!
The idea of flipping a copy for Side #2 will still work, but the stuff nested inside has to use distinct objects for each board. Every instance of a component is identical to all others!
On another level, be aware that intersect with always places Edges in whatever edit context is open at the time. So, for example, if you just select the sloping plane and invoke intersect-with model, the Edges will be in the model, not within any of the nested components or groups. There are two ways you can get them there. Probably the best is to Edit->Copy the sloped plane, open the nested components down to the innermost, do Edit->Paste in Place, then select the pasted copy and do intersect with context. That will put new Edges in that component and you can clean up without affecting anything else. You have to repeat this for each of the nested components, but that’s pretty much inevitable since each of them needs to be edited. The alternative is to do the intersect with model and copy then paste-in-place the edges inside each nested component. This is messier because the copy contains the intersections with everything - a lot more to clean up each time.