Among the most fundamental observables of nucleon structure, electromagnetic form factors are a crucial benchmark for modern calculations describing the strong interaction dynamics of the nucleon's quark constituents; indeed, recent proton data have attracted intense theoretical interest. In this Letter, we report new measurements of the proton electromagnetic form factor ratio using the recoil polarization method, at momentum transfers Q2=5.2, 6.7, and 8.5 GeV2. By extending the range of Q2 for which G(E)(p) is accurately determined by more than 50%, these measurements will provide significant constraints on models of nucleon structure in the nonperturbative regime.