The π + Σ + , π + Ξ 0 , K + p , K + n , and ¯¯¯¯ K 0 Ξ 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 π + Σ + = − 0.197 ± 0.017     fm , and a π + Ξ 0 = − 0.098 ± 0.017     fm , where the comprehensive error includes statistical and systematic uncertainties.