Uniform solvability at one for relative $(\varphi_2,\nabla_2)$-modules

Let $I=\{1,2\}$, let $M$ be a $\Phi$-equivariant $F$-isocrystal $(M,\varphi,\varphi_1,\varphi_2)$ in the category $\overline{h}_{\mathrm{con},I/\varphi_1,t_1=t_2=0}^{\flat,\mathrm{holo},\varphi}$, and regard it as a relative $(\varphi_2,\nabla_2)$-module over

$$\mathrm{Sp}(\pi_{\mathrm{con},\mathbb{Z}_p[[t_1]],t_1=0})/\varphi_1\widehat{\otimes}_{\mathbb{Q}_p}\pi_{\mathrm{con},\mathbb{Z}_p[[t_2]],t_2=0}.$$

For each fiber $M_{x_1}$ over $\mathrm{Sp}(\pi_{\mathrm{con},\mathbb{Z}_p[[t_1]],t_1=0})/\varphi_1$, write $R(M_{x_1},\rho_2)$ for its radius of convergence. Uniform solvability conjecture. The module $M$ is solvable at $1$ uniformly with respect to every fiber, namely

$$\lim_{\rho_2\rightarrow 1}R(M_{x_1},\rho_2)\rho_2^{-1}=1$$

uniformly for all such $x_1$. This is an expected relative Robba-ring property inspired by Kedlaya's work; the supplied text gives no proof or resolution.