I would create a blue surf made by two section (the top circle and the bottom sinuodoid curve) and some intersection curves that define the side wall.
And I would do it in ordered to make it much easier to adjust to what needed.
After that create geometry with a boolean operation.
Yeah, definitely in ordered, but I probably wouldn't try to imitate the edge where the shape intersects the cone. That's really just a by-product of the shape.
One thing you can do would be to take cross sections at various places and use those sections to help build your bluesurf. The sections should be perpendicular to the guide curves as much as possible.