We investigate an effective Hamiltonian for QCD at large s, in which longitudinal gauge degrees of freedom are suppressed, but not eliminated. In an axial gauge the effective field theory is a set of coupled (1+1)-dimensional principal-chiral models, which are completely integrable. The confinement problem is solvable in this context, and we find the longitudinal and transverse string tensions with techniques already used for a similar Hamiltonian in (2+1)-dimensions. We find some a posteriori justification for the effective Hamiltonian as an eikonal approximation. Hadrons in this approximation consist of partons, which are quarks and soliton-like excitations of the sigma models. Diffractive hadron-hadron scattering appears primarily due to exchange of longitudinal flux between partons.