Hey TAK,
You need to work with the Coordinate Manager (not the one in the Attribute Manager.)
If you like to have a flat line, you need to know the level on which they should be. Position.Z=0.0 in your case perhaps. The following is not my idea way to work, but you ask for the fast method.
As I mentioned above, you use the “Extrude” only a tiny bit, e.g., Offset=0.1 or 0.01. Try first to use a large numbr e.g., 8 to see where they go, find an average Edge Angle ( -35º perhaps) to have them from a z view (right in your case) nearly equally extruded, then take that step back and use the first 0.1 or 0.01 extrude with that angle. Then set the Z size in that Coordinate Manager to zero and AFTER that, the P.Z position to 0.0 (always while the selection is still given!) Repeat this exactly one more. (Of course 0º Edge Angle)
Do another Extrude (offset larger now, I used 4.0 in the image below) and “size” and then position. You get a “coast line that follows of course the topology of the given model. The smaller the first two steps, the more precise the is the curve of the coast line.
One word to the Normals, the orientation of the Polygon Normals was OK, all share the same direction. The polygons itself have quite a variety of direction. Some would even undercut each other if just extruded in one step. I think I would have drawn a Spline Guide and created the Polygons manually. With no long thoughts about that. Extrude is nice and a great tool, but for some stuff, they are not build for. You could go even with the fast method above and use the resulting points of the new coastline to set the polygons. Just my two cents.
All the best
Sassi