We explore different multi-stage and multi-constraint modeling strategies using the Hybrid Reverse Monte Carlo (HRMC) technique to develop realistic models for the amorphous structure of silicon carbide derived-carbon, and investigate the effect of modeling parameters on the development of nano-structural features of the constructed models. It is shown that application of long simulations with slow thermal quench rate is essential for modeling of amorphous structures. Nevertheless, very slow quenching rates are shown to lead to the formation of configurations with large fraction of sp2 carbon, lacking the level of disorder required to match structure-related experimental data. The predicted gas adsorption isotherms are very sensitive to the pore size distribution (PSD), thus the final structure must reasonably reproduce the total pore volume and pore size distribution of the experimental sample. The frequently-observed strong first peak of the DFT-based PSD obtained from argon adsorption is shown to be an artifact of argon inaccessibility. Pore accessibility analysis of the constructed models, as well as MD simulations of gas transport demonstrate that the HRMC constructed structures contain short-range structural anisotropy, however the models are successful in capturing the long range internal energy barriers of amorphous carbon for methane.