It seems to me that drawing the curve when it overlaps creates areas to be viewed independently. These must then also be triangulated independently. In your last picture you can see that some triangles go through the area that is obviously not to be filled.
Arbitrarily bordered areas can be filled with a general triangulation algorithm. But then you have to recalculate each time, which is time-consuming.
Have a look at
Inner Geometry (Triangulation)
Addon for triangulation of implicit surfaces/ forms with holes.
Maybe you can do something with it?