  The vibrational branching ratios from the lowest excited electronic state for
$\textrm{SrOCH}_3$, $\textrm{SrNH}_2$, and $\textrm{SrSH}$ are measured at the
$< 0.1\%$ level. Spectra are obtained by driving the $\tilde{X} - \tilde{A}$
transitions and dispersing the fluorescence on a grating spectrometer. We also
perform $\textit{ab initio}$ calculations for the energies of vibrational
levels relevant for laser cooling, as well as branching ratios to support the
interpretations of all molecular spectra. Symmetry group analysis is applied in
conjunction with our data to study rotational closure in these molecules. These
analyses indicate favorable prospects for laser cooling $\textrm{SrNH}_2$ and
other similar alkaline-earth(-like) amides for future beyond the Standard Model
physics searches using polyatomic molecules with long-lived parity doublets.
