The Poncelet inellipse concentricity conjecture for Simson-line envelopes

Let a Poncelet triangle family be inscribed in a circle with inconic or caustic, and let $F$ vary over the circumcircle. For each $F$, let $W$ be the envelope point of the corresponding Simson lines. Inellipse concentricity conjecture. Over all $F$, the locus of $W$ is an ellipse concentric with the inconic or caustic. The surrounding discussion reports this as a further geometric pattern for circle-inscribed Poncelet families; its general validity remains open.