Look at TIG's "extrusion tools" plugin. Note you may have to make the begining and end shapes into "Curves" by welding the parts together. If that end is single line. Break it to min. two parts and weld it back. With Extrude edges by rails, that setup will give you a shape that diminishes to a flat line.If you wanted it to remain curved-top throughout you have to consider an ending profile.