Two approaches, the outgoing wave variational principle (OWVP) and R-matrix propagation (RMProp), are presented for quantum dynamics calculations of inelastic scattering in systems involving two coupled potential energy surfaces (PES). The two formalisms are applied to Na(3p 2P) collisions with H2 at a total energy of 2.426 eV with zero and unit total angular momentum. This provides a challenging test case because the accessible region of the excited-state potential energy surface intersects the ground-state surface conically and involves H-H internuclear distances that are far larger than their equilibrium values in the ground state. We present the details of the formalisms for treating coupled surfaces, and we present converged results for the quenching probability and final vibrational-rotational quantum state distributions of the quenching agent. Convergence of the transition probabilities is established by convergence checks within each formalism, by obtaining the same results with laboratory-frame and body-frame basis functions in the OWVP formalism, and by obtaining the same results with the OWVP as with RMProp.