Hi Marine - This may or may not be accurate enough - I see I did not use a ShortPath in my test, which makes a difference - I did use that on the cone example. The issue is, for a straight plank to lie cleanly on a surface it has to, I think, follow a geodesic curve, and I neglected to do that in this case.
In any case, either way, the base surface has to be G2 , curvature continuous, for this to work cleanly. Yours is several surfaces that are tangent (well not quite, but close) so you can see in my file that I recreated the surface from a single G2 curve that closely (please check ho closely, the curves are in the file) approximates your roof surfaces:

Now, using a geodesic (ShortPath command) make a curve in the direction of the planks - note that the curve will find its own way along the surface between start and end points. Note I made my surface oversized a bit too.
Now, OffsetCrvOnSrf the curve by the width of the plank - 20cm

Mark one end of both curves with points (the distance/direction from one point to the other is the distance to copy the plank when it’s done and you want to fill the entire surface) and then make lines perpendicular at the ends and Trim to make the ‘plank’
Now, Loft the curves together using StraightSections and Rebuild with maybe 24 points:
That is the base surface for one plank - by using ShortPath for the initial curve, UnrollSrf of this surface will make a straight plank - that is this shape can be created by bending a straight plank, which is what we want.
OffsetSrf > Solid = Yes to get thickness
Copy the plank as needed from one of the earlier marker points at the ends of the curve to the other.
@Marine1 - you can do this with your tangent surfaces but it is a bit more complicated.
-Pascal