New Faddeev-Yakubovsky calculations for light $\ensuremath{\Lambda}\ensuremath{\Lambda}$ hypernuclei are presented in order to assess the self-consistency of the $\ensuremath{\Lambda}\ensuremath{\Lambda}$-hypernuclear binding-energy world data and the implied strength of the $\ensuremath{\Lambda}\ensuremath{\Lambda}$ interaction, in the wake of recent experimental reports on ${}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{ 4}\mathrm{H}$ and ${}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{ 6}\mathrm{He}.$ Using Gaussian soft-core simulations of Nijmegen one-boson-exchange model interactions, the Nijmegen soft-core model NSC97 simulations are found close to reproducing the recently reported binding energy of ${}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{ 6}\mathrm{He},$ but not those of other species. For stranger systems, Faddeev calculations of light $\ensuremath{\Lambda}\ensuremath{\Xi}$ hypernuclei, using a simulation of the strongly attractive $\ensuremath{\Lambda}\ensuremath{\Xi}$ interactions due to the same model, suggest that ${}_{\ensuremath{\Lambda}\ensuremath{\Xi}}^{ 6}\mathrm{He}$ marks the onset of nuclear stability for $\ensuremath{\Xi}$ hyperons.