The circledsteps package (based on TiKZ) defines some rectangle with rounded smal sides for long terms.
However, if you really want an ellipse, pstricks defines a \psovalboxfor that:
Needed assumptions on F, since we know $\lambda_1^*$ must lie ...
Based on the solution you provide, why don't you use the shape library to draw an ellipse instead of a circle?
OK, so instead of editing my previous answer (which was meant to give a hint on even odd rule with hobby closed curve, when the question was very unclear), I add a new one which I would delete if it's not what OP wants.
So basically, what you seem to ask for is a way to fill a clipped part of a shape, like the following: