I tried all sorts of ways to make this work in the weekend but I didn't succeed. The problem is shapekeys and modifiers don't play together nicely. If I apply the bevel modifier after the shapekeys are created, then only one of the shapekeys are modified. If I apply the modifier before the two shapekeys are created, then I face the hard 3D problem of transforming the beveled shape to the other desired beveled shape.
So basically I would like to have a smooth animation of a mesh object that transforms from this shape:
to this shape:
while the shape is being extruded and beveled.