Background: Interest in the behavior of nucleon electromagnetic form factors at large momentum transfers has steadily increased since the discovery, using polarization observables, of the rapid decrease of the ratio GEp/GMp of the proton's electric and magnetic form factors for momentum transfers Q21 GeV2, in strong disagreement with previous extractions of this ratio using the traditional Rosenbluth separation technique. Purpose: The GEp-III and GEp-2γ experiments were carried out in Jefferson Laboratory's (JLab's) Hall C from 2007 to 2008, to extend the knowledge of GEp/GMp to the highest practically achievable Q2 given the maximum beam energy of 6 GeV and to search for effects beyond the Born approximation in polarization transfer observables of elastic ∫ - p scattering. This article provides an expanded description of the common experimental apparatus and data analysis procedures, and reports the results of a final reanalysis of the data from both experiments, including the previously unpublished results of the full-acceptance dataset of the GEp-2γ experiment. Methods: Polarization transfer observables in elastic ∫ - p→∫ - scattering were measured at central Q2 values of 2.5, 5.2, 6.8, and 8.54 GeV2. At Q2=2.5GeV2, data were obtained for central values of the virtual photon polarization parameter ϵ of 0.149, 0.632, and 0.783. The Hall C High Momentum Spectrometer detected and measured the polarization of protons recoiling elastically from collisions of JLab's polarized electron beam with a liquid hydrogen target. A large-acceptance electromagnetic calorimeter detected the elastically scattered electrons in coincidence to suppress inelastic backgrounds. Results: The final GEp-III data are largely unchanged relative to the originally published results. The statistical uncertainties of the final GEp-2γ data are significantly reduced at ϵ=0.632 and 0.783 relative to the original publication. Conclusions: The final GEp-III results show that the decrease with Q2 of GEp/GMp continues to Q2=8.5GeV2, but at a slowing rate relative to the approximately linear decrease observed in earlier Hall A measurements. At Q2=8.5GeV2, GEp/GMp remains positive but is consistent with zero. At Q2=2.5GeV2, GEp/GMp derived from the polarization component ratio R-Pt/P shows no statistically significant ϵ dependence, as expected in the Born approximation. On the other hand, the ratio P""/P""Born of the longitudinal polarization transfer component to its Born value shows an enhancement of roughly 1.7% at ϵ=0.783 relative to ϵ=0.149, with ≈2.2σ significance based on the total uncertainty, implying a similar effect in the transverse component Pt that cancels in the ratio R.