Hi Alex, the "bowl cutting surface" method would go something like this - you'd need to make one large surface that submerges down into the other ones something like this (in this case here I've done a rail revolve using half an ellipse as the rail):



Then with those pieces pushing through each other you can use Edit > Trim to slice them all up and remove excess area to end up with this:



In this method you have to concentrate more effort on making the cutting surface to have the kind of shape you want (the one I did here is not quite right), but it does leave a continuous result since the whole filled in area comes from one single surface.

- Michael