In this work, we introduce a classical trajectory Monte Carlo (CTMC) methodology, specially conceived to provide a more accurate representation of charge-exchange processes between highly charged ions and H(1s) and H* (n=2). These processes are of particular relevance in power fusion reactor programs, for which charge-exchange spectroscopy has become a useful plasma diagnostics tool. To test the methodology, electron-capture reactions from these targets by C6+,N7+, and O8+ are studied at impact energies in the 10-150keV/amu range. State-selective cross sections are contrasted with those predicted by the standard microcanonical formulation of the CTMC method, the CTMC method with an energy variation of initial binding energies that produces an improved radial electron density, and the atomic orbital close-coupling method. The present results are found in to be much better agreement with the quantum-mechanical results than the results of former formulations of the CTMC method.