Excitation functions for the natW(3He, x)184m,gRe nuclear reactions were measured from respective thresholds up to 55 MeV by using a conventional stacked-foil activation technique combined with HPGe γ-ray spectroscopy. Individual cross-section values for the production of 184mRe and 184gRe were separated using a proper mathematical method based on their interference-free characteristic gamma lines and the data are reported here for the first time. The default parameters of recently developed nuclear model code TALYS-1.96 were found to be unable to reproduce the excitation functions, hence cannot provide 184mRe/184gRe isomeric cross-section ratios consistent with the experimental results. However, the adjustment of the level density model and optical model potentials together with some other parameters, such as the spin cut-off parameter, were found to be effective to reproduce the measured excitation functions. A similar parameter adjustment may be useful to reproduce the excitation functions of like unusual isomeric pairs, especially when the metastable state is longer-lived than the ground state. The reported cross-sections and the model calculation show interesting in the understanding of the nuclear reaction mechanisms as well as for the improvement of nuclear model codes for accurate prediction of nuclear reaction cross-sections where the experimental data are scarce, or an expensive experiment is required to obtain experimental data.