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The GEp-III and GEp-2$\gamma$ experiments were carried out in Jefferson Lab's(JLab's) Hall C from 2007-2008, to extend the knowledge of $G_E^p/G_M^p$ to thehighest practically achievable $Q^2$ and to search for effects beyond the Bornapproximation in polarization transfer observables of elastic $\vec{e}p$scattering. This article reports an expanded description of the commonexperimental apparatus and data analysis procedure, and the results of a finalreanalysis of the data from both experiments, including the previouslyunpublished results of the full-acceptance data of the GEp-2$\gamma$experiment. The Hall C High Momentum Spectrometer detected and measured thepolarization of protons recoiling elastically from collisions of JLab'spolarized electron beam with a liquid hydrogen target. A large-acceptanceelectromagnetic calorimeter detected the elastically scattered electrons incoincidence to suppress inelastic backgrounds. The final GEp-III data arelargely unchanged relative to the originally published results. The statisticaluncertainties of the final GEp-2$\gamma$ data are significantly reduced at$\epsilon = 0.632$ and $0.783$ relative to the original publication. Thedecrease with $Q^2$ of $G_E^p/G_M^p$ continues to $Q^2 = 8.5$ GeV$^2$, but at aslowing rate relative to the approximately linear decrease observed in earlierHall A measurements. At $Q^2 = 2.5$ GeV$^2$, the proton form factor ratio$G_E^p/G_M^p$ shows no statistically significant $\epsilon$-dependence, asexpected in the Born approximation. The ratio $P_\ell/P_\ell^{Born}$ of thelongitudinal polarization transfer component to its Born value shows anenhancement of roughly 1.4\% at $\epsilon = 0.783$ relative to $\epsilon =0.149$, with $\approx 1.9\sigma$ significance based on the total uncertainty,implying a similar effect in the transverse component $P_t$ that cancels in theratio $R$.

Polarization Transfer Observables in Elastic Electron Proton Scattering at $Q^2 = $2.5, 5.2, 6.8, and 8.5 GeV$^2$