I checked length snapping too. I also cleaned up the drawing best I could. Front faces, eliminated other geometry. Co-planar faces in both groups. As I said I found that I could avoid the hidden lines being created but drape didn’t work so well.
I don’t think it has to do with having all your geometry being square or perfect in some sense. The sandbox drape tool CAN work on complex meshes, BUT it is not perfect, SketchUp is not perfect. Sometimes it doesn’t catch everything correctly.
I’ve seen other cases where SketchUp thinks a face is a face but NOT. It can close the face but only with manual “fixing” and lose it again easily. This creation of hidden lines is not that common, may have something to do with the other plugins you tried. I’d move on. (Or like the “real world”, this could be just another instance of the uncertainty principle. )
On an aside. I don’t use the tool much myself. It doesn’t really serve a purpose in my workflow. If I must cut terrain it is after I’ve worked out a foundation and use intersect faces on a portion of the terrain near the house, if I haven’t already replaced it with new grading.