  We examine the efficacy of pion exchange models to simultaneously describe
leading neutron electroproduction at HERA and the $\bar{d}-\bar{u}$ flavor
asymmetry in the proton. A detailed $\chi^2$ analysis of the ZEUS and H1 cross
sections, when combined with constraints on the pion flux from Drell-Yan data,
allows regions of applicability of one-pion exchange to be delineated. The
analysis disfavors several models of the pion flux used in the literature, and
yields an improved extraction of the pion structure function and its
uncertainties at parton momentum fractions in the pion of $4 \times 10^{-4}
\lesssim x_\pi \lesssim 0.05$ at a scale of $Q^2$=10 GeV$^2$. Based on the fit
results, we provide estimates for leading proton structure functions in
upcoming tagged deep-inelastic scattering experiments at Jefferson Lab on the
deuteron with forward protons.
