  The $\gamma p \to K^+ \pi^0 \Lambda$ and $\gamma p \to K^+ \pi \Sigma $
reactions are studied in the kinematic region where the $\pi^0 \Lambda$(1116)
and $\pi\Sigma$(1192) pairs originate dominantly from the decay of the
$\Sigma$(1385) and $\Lambda$(1405) resonances. We consider laboratory photon
energies around 2 GeV, i.e. total center of mass energies above the known
resonance region. We compute the t-channel kaon-exchange contribution to these
reactions using $K^- p \to \pi^0 \Lambda$ and $K^- p \to \pi \Sigma$ amplitudes
calculated in the framework of a chiral coupled-channel effective field theory
of meson-baryon scattering. We extract from the calculated cross section the
gauge-invariant double kaon pole term. We find this term to be large and likely
to drive significantly the $\gamma p \to K^+ \pi^0 \Lambda$ and $\gamma p \to
K^+ \pi \Sigma $ reactions in the kinematics under investigation. Accurate
measurements of t-distributions for these processes, in progress or planned at
ELSA and at SPring-8, are needed to confirm this expectation and assess the
possibility of studying antikaon-nucleon dynamics just below threshold through
these reactions.
