Double charge exchange (DCE) reactions could provide experimentally driven information about nuclear matrix elements of interest in the context of neutrinoless double-beta decay. To achieve this goal, a detailed description of the reaction mechanism is mandatory. This requires the full characterization of the initial and final-state interactions, which are poorly known for many of the projectile-target systems involved in future DCE studies. Among these, we intend to study the Ne-20 + Te-130 and O-18 + Sn-116 systems at 15.3 AMeV, which are particularly relevant due to their connection with the Te-130 -> Xe-130 and Cd-116 -> Sn-116 double-beta decays. We measure the elastic and inelastic scattering cross-section angular distributions and compare them with theoretical calculations performed in the optical model, one-step distorted wave Born approximation, and coupled-channel approaches using the Sao Paulo double-folding optical potential. A good description of the experimental data in the whole explored range of transferred momenta is obtained provided that couplings with the 2(1)(+) states of the projectile and target are explicitly included within the coupled-channel approach. These results are relevant also in the analysis of other quasi-elastic reaction channels in these systems, in which the same couplings should be included.