  Precise measurements of the proton electromagnetic form factor ratio $R =
\mu_p G_E^p/G_M^p$ using the polarization transfer method at Jefferson Lab have
revolutionized the understanding of nucleon structure by revealing the strong
decrease of $R$ with momentum transfer $Q^2$ for $Q^2 \gtrsim 1$ GeV$^2$, in
strong disagreement with previous extractions of $R$ from cross section
measurements. In particular, the polarization transfer results have exposed the
limits of applicability of the one-photon-exchange approximation and
highlighted the role of quark orbital angular momentum in the nucleon
structure. The GEp-II experiment in Jefferson Lab's Hall A measured $R$ at four
$Q^2$ values in the range 3.5 GeV$^2 \le Q^2 \le 5.6$ GeV$^2$. A possible
discrepancy between the originally published GEp-II results and more recent
measurements at higher $Q^2$ motivated a new analysis of the GEp-II data. This
article presents the final results of the GEp-II experiment, including details
of the new analysis, an expanded description of the apparatus and an overview
of theoretical progress since the original publication. The key result of the
final analysis is a systematic increase in the results for $R$, improving the
consistency of the polarization transfer data in the high-$Q^2$ region. This
increase is the result of an improved selection of elastic events which largely
removes the systematic effect of the inelastic contamination, underestimated by
the original analysis.
