  We report the theoretical prediction of two high-performing hydride
superconductors BaSiH$_8$ and SrSiH$_8$. They are thermodynamically stable
above pressures of $130$ and $174\,\text{GPa}$, respectively, and metastable
below that. Employing anharmonic phonon calculations, we determine the minimum
pressures of dynamical stability to be around $3\,\text{GPa}$ for BaSiH$_8$ and
$27\,\text{GPa}$ for SrSiH$_8$, and using the fully anisotropic
Migdal-Eliashberg theory, we predict $T_\text{c}$'s around $71$ and
$126\,\text{K}$, respectively. We also introduce a method to estimate the
lowest pressure of synthesis, based on the calculation of the enthalpy barriers
protecting the BaSiH$_8$ $Fm\bar{3}m$ structure from decomposition at various
pressures. This $kinetic$ pressure threshold is sensibly higher than the one
based on $dynamic$ stability, but gives a much more rigorous limit for
synthesizability.
