Weaker Rudominer–Steel conjecture with an existing omega-one

Assume $\mathrm{ZF}+\mathsf{AD}^{L(\mathbb R)}$. Let $M$ be a $(0,\omega_1)$-iterable countable $\omega$-small premouse satisfying “$\omega_1$ exists”. Then there are $\gamma$, $\beta$, and $\pi$ as in the Rudominer–Steel conjecture, except that $\pi$ is only required to be $\Sigma_1$-elementary and the wellorder of $\mathbb R^M$ is required to be definable over $\mathcal{S}_\gamma(\mathbb R^M)$ from some $x\in\mathbb R^M$. Weaker Rudominer–Steel conjecture. Such $\gamma$, $\beta$, and $\pi$ exist. This is explicitly presented as a weaker variant of the Rudominer–Steel conjecture, with the additional assumption that $M$ models that $\omega_1$ exists; the supplied text gives no resolution status.