(Non-answers "I've never done this before"; and 'interesting' asides "There are all these features that I've rarely use and don't help solve your problem" uninvited.)
In the attached model, there are these curves, which are one full ellipse and two half ellipses:
Two share a semi-major axis; two share a semi-minor axis, but all three ellipses are different.
(In reality, the two half curves will be catenery curves, but this suffices as an example.)
The problem is to create a surface like this:
But without the seams and obvious distortions.