Boundedness conjecture for simply connected period-two shell components

Let $\Lambda$ be a dynamically natural slice for a family of meromorphic maps $\{f_\lambda,\ \lambda \in \Lambda\}$ in $\mathcal{M}_\infty$ in the strict sense. Let $\Omega \subset \Lambda$ be a simply connected shell component of period $k=2$. Boundedness conjecture. Then $\Omega$ is bounded.

The conjecture arises from examples of dynamically natural slices in which all simply connected shell components of period greater than one are bounded, contrasting with the always-unbounded period-one shell components. Its status is not resolved in the supplied text.