The problem is not insurmountable, but there's a lot of work involved. My suggestion for such a mathematically complex shape is to calculate the Lat and Long of 360 Radial / Distances (609 nm) from the contingency airport, and join them. It works well in other plotting applications where the shape is complex, and the calculation of the series of Lat and Longs are 'straight' spherical trigonometry.
It probably has a name, but for the moment, in your honour, I've labeled it the
"Compressorstalloidodrome.
Lots of luck,
Old Smokey