  Consequences of increasing the binding energy of the hypertriton ground state
${_{\Lambda}^3}{\rm H}(J^P={\frac{1}{2}}^+)$ from the emulsion value $B^{\rm
EMUL}_{\Lambda}({_{\Lambda}^3}{\rm H}_{\rm g.s.})$=0.13$\pm$0.05 MeV to the
STAR value $B^{\rm STAR}_{\Lambda}(^{3}_{\Lambda}{\rm H}) = (0.41\pm 0.12 \pm
0.11)$ MeV are studied for $s$-shell hypernuclei within a pionless EFT approach
at leading order, constrained by the binding energies of the $0^+$ and $1^+$
${_{\Lambda}^4} {\rm H}$ states. The stochastic variational method is used in
bound-state calculations, whereas the inverse analytic continuation in the
coupling constant method is used to locate $S$-matrix poles of continuum
states. It is found that the $\Lambda nn({\frac{1}{2}}^+)$ resonance becomes
broader and less likely to be observed experimentally, whereas the
${_{\Lambda}^3}{\rm H}({\frac{3}{2}}^+)$ spin-flip virtual state moves closer
to the $\Lambda d$ threshold to become a shallow bound state for specific
$\Lambda N$ interaction strengths. The effect of such a near-threshold
${_{\Lambda}^3}{\rm H}({\frac{3}{2}}^+)$ state on femtoscopic studies of
$\Lambda$-deuteron correlations, and its lifetime if bound, are discussed.
Increasing $B_{\Lambda}({_{\Lambda}^3} {\rm H}_{\rm g.s.})$ moderately, up to
$\sim$0.5 MeV, hardly affects calculated values of
$B_{\Lambda}({_{\Lambda}^5}{\rm He})$.
