We present an update to the framework called SImulator of GAlaxy Millimeter/submillimeter Emission (S\'IGAME). S\'IGAME derives line emission in the far-infrared (FIR) for galaxies in particle-based cosmological hydrodynamics simulations by applying radiative transfer and physics recipes via a post-processing step after completion of the simulation. In this version, a new technique is developed to model higher gas densities by parametrizing the gas density probability distribution function (PDF) in higher resolution simulations for use as a look-up table, allowing for more adaptive PDFs than in previous work. S\'IGAME v3 is tested on redshift z = 0 galaxies drawn from the SIMBA cosmological simulation for eight FIR emission lines tracing vastly different interstellar medium phases. Including dust radiative transfer with SKIRT and high resolution photo-ionization models with Cloudy, this new method is able to self-consistently reproduce observed relations between line luminosity and star formation rate in all cases, except for [NII]122, [NII]205 and [OI]63, the luminosities of which are overestimated by median factors of 1.6, 1.2 and 1.2 dex, respectively. We attribute the remaining disagreement with observations to the lack of precise attenuation of the interstellar light on subgrid scales (≲200 pc) and differences in sample selection.