  Hybrid/exotic meson spectroscopy searches at Jefferson Lab require the
accurate theoretical description of the production mechanism in peripheral
photoproduction. We develop a model for $\pi\Delta$ photoproduction at high
energies ($5 \leq E_{\text{lab}} \leq 16~\text{GeV}$) that incorporates both
the absorbed pion and natural-parity cut contributions. We fit the available
observables, providing a good description of the energy and angular
dependencies of the experimental data. We also provide predictions for the
photon beam asymmetry of charged pions at $E_{\text{lab}} = 9~\text{GeV}$ which
is expected to be measured by GlueX and CLAS12 experiments in the near future.
