Cutting/creating surface a between 2 existing edge loops ?

I have a cap in Aluminium like this

The long axis of the base elipse is 54mm.

I want to create one about twice as big. I have this.

An extruded ellipse with the surface drawn on top (top surface is 2 x offset centre ellipses , trimmed)

I cannot figure how to create a surface between the base ellipse and the top surface and then cut. I also tried removing the solid itself and using fill from the 2 x surfaces/surface edges and all sorts of other attempts. I hope someone more clever than me can help me figure out how to do this, it would be much appreciated.