Beam-recoil transferred polarizations for the exclusive $vec{e}p to eK^+ vec{Lambda},vec{Sigma}^0$ reactions have been measured using the CLAS spectrometer at Jefferson Laboratory. New measurements have been completed at beam energies of 4.261 and 5.754 GeV that span a range of momentum transfer $Q^2$ from 0.7 to 5.4 GeV$^2$, invariant energy $W$ from 1.6 to 2.6 GeV, and the full center-of-mass angular range of the $K^+$ meson. These new data add to the existing CLAS $K^+Lambda$ measurements at 2.567 GeV, and provide the first-ever data for the $K^+Sigma^0$ channel in electroproduction. Comparisons of the data with several theoretical models are used to study the sensitivity to s-channel resonance contributions and the underlying reaction mechanism. Interpretations within two semi-classical partonic models are made to probe the underlying reaction mechanism and the $sbar{s}$ quark-pair creation dynamics.
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