The (${\mathrm{\ensuremath{\pi}}}^{+}$,${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$) double-charge-exchange reaction for pion energies of 200 to 1400 MeV is calculated with a zero-parameter Glauber theory that includes spin flip and pion absorption. Differential cross sections and excitation functions are obtained for $^{14}\mathrm{C}$ and $^{18}\mathrm{O}$ targets. Results for ${\mathit{T}}_{\mathrm{\ensuremath{\pi}}}$=300--525 MeV are compared with recent experimental results and suggest a new quenching process. We have calculated effects of medium polarization on the isovector pion operator and find a strong reduction in good agreement with data. A pronounced dip in the cross section near ${\mathit{T}}_{\mathrm{\ensuremath{\pi}}}$=1300 MeV offers a unique testing ground for unconventional mechanisms.