How to avoid creating hidden lines from intersecting shapes

I couldn’t get your example model to show any stress lines, but still you could try the extension that sWilliams made, here:

The file you download is sw_flatten_to_calculated_plane.rbz. Install that, then select a set of faces and edges that are supposed to be coplanar, but might not be, then choose the extension in the Extensions menu. It may prevent stress lines from occurring, or get rid of them if they are already there.