  [Background] Above the nucleon resonance region, the $N(e,e'\pi^\pm)N'$ data
cannot be explained by conventional hadronic models. For example, the observed
magnitude of the transverse cross section is significantly underestimated in a
framework with Reggeized background amplitudes.
  [Purpose] Develop a phenomenological framework for the $N(e,e'\pi^\pm)N'$
reaction at high invariant mass $W$ and deep photon virtuality $Q^2$.
  [Method] Building on the work of Kaskulov and Mosel, a gauged pion-exchange
current is introduced with a running cutoff energy for the proton
electromagnetic transition form factor. A new transition form factor is
proposed. It respects the correct on-shell limit, has a simple physical
interpretation and reduces the number of free parameters by one.
  [Results] A study of the $W$ dependence of the $N(e,e'\pi^\pm)N'$ lends
support for the newly proposed transition form factor. In addition, an improved
description of the separated and unseparated cross sections at $-t \lesssim 0.5
\;\text{GeV}^2$ is obtained. The predictions overshoot the measured unseparated
cross sections for $-t > 0.5 \;\text{GeV}^2$. Introducing a strong hadronic
form factor in the Reggeized background amplitudes brings the calculations
considerably closer to the high $-t$ data.
  [Conclusions] Hadronic models corrected for resonance/parton duality describe
the separated pion electroproduction cross sections above the resonance region
reasonably well at low $-t$. In order to validate the applicability of these
models at high $-t$, separated cross sections are needed. These are expected to
provide a more profound insight into the relevant reaction mechanisms.
