  We use a recently developed dispersive approach to compute the two-photon
exchange (TPE) correction to elastic electron-proton scattering, including
contributions from hadronic $J^P=1/2^\pm$ and $3/2^\pm$ resonant intermediate
states below~1.8~GeV. For the transition amplitudes from the proton ground
state to the resonant excited states we employ new exclusive meson
electroproduction data from CLAS at $Q^2 \lesssim 5$~GeV$^2$, and we explore
the effects of both fixed and dynamic widths for the resonances. Among the
resonant states, the $N(1520)~\!3/2^-$ becomes dominant for $Q^2 \gtrsim
2$~GeV$^2$, with a sign opposite to the comparably sized $\Delta(1232)~\!3/2^+$
contribution, leading to an overall increase in the size of the TPE correction
to the cross section relative to the nucleon only contribution at higher $Q^2$
values. The results are in good overall agreement with recent $e^+ p$ to $e^-
p$ cross section ratio and polarization transfer measurements, and provide
compelling evidence for a resolution of the electric to magnetic form factor
ratio discrepancy.
