  The $\pi^+\Sigma^+$, $\pi^+\Xi^0$, $K^+p$, $K^+n$, and $\overline{K}{}^0
\Xi^0$ scattering lengths are calculated in mixed-action Lattice QCD with
domain-wall valence quarks on the asqtad-improved coarse MILC configurations at
four light-quark masses, and at two light-quark masses on the fine MILC
configurations. Heavy Baryon Chiral Perturbation Theory with two and three
flavors of light quarks is used to perform the chiral extrapolations. To the
order we work in the three-flavor chiral expansion, the kaon-baryon processes
that we investigate show no signs of convergence. Using the two-flavor chiral
expansion for extrapolation, the pion-hyperon scattering lengths are found to
be $a_{\pi^+\Sigma^+}=-0.197\pm0.017$ fm, and $a_{\pi^+\Xi^0}=-0.098\pm0.017$
fm, where the comprehensive error includes statistical and systematic
uncertainties.
