Non-simplicity of formal contact isotopy classes of isocontact embeddings

Let $n$ be a positive integer, and let $(S^{2n+1},\xi_\text{st})$ be the standard contact sphere. Consider isocontact embeddings of $(\partial T^*S^n,\xi_\text{st})$ into $(S^{2n+1},\xi_\text{st})$, where $\partial T^*S^n$ denotes the unit cosphere bundle with its standard contact structure. Two such embeddings are formally contact isotopic when they are connected by an isotopy through formally isocontact embeddings. Non-simplicity conjecture. There exist infinitely many formally contact isotopic isocontact embeddings of $(\partial T^*S^n,\xi_\text{st})$ into $(S^{2n+1},\xi_\text{st})$ which are not contact isotopic. The claim would give infinitely many distinct contact-isotopy classes within a single formal class; the supplied source does not provide evidence resolving this conjecture.