Spin transfer observables for the strangeness-production reaction Antiproton-Proton -> Antilambda-Lambda have been measured by the PS185 collaboration using a transversely-polarized frozen-spin target with an antiproton beam momentum of 1.637 GeV/c at the Low Energy Antiproton Ring at CERN. This measurement investigates observables for which current models of the reaction near threshold make significantly differing predictions. Those models are in good agreement with existing measurements performed with unpolarized particles in the initial state. Theoretical attention has focused on the fact that these models produce conflicting predictions for the spin-transfer observables D_{nn} and K_{nn}, which are measurable only with polarized target or beam. Results presented here for D_{nn} and K_{nn} are found to be in disagreement with predictions from existing models. These results also underscore the importance of singlet-state production at backward angles, while current models predict complete or near-complete triplet-state dominance.