Now guys are we talking about the stamp tool or the drape tool?
True that for the drape tool, simple 2d linework is the ideal.
For the stamp tool however, 3d shapes should also work - though with some limitations: they shouldn't have vertical edges (otherwise the TIN gets screwed up). Also there seems to be a kind of limitation in the complexity of the shape you want to stamp in and in your model that is quite a complex shape.
If you really want to stamp it on that surface, make just an outline and a single face of that shape and try that. After that you can just place your existing model on top of the stamped, flat surface.