This paper presents a study of sodium-decorated circumcircumcoronene, a large polycyclic aromatic hydrocarbon (PAH) regarded as a graphene prototype, and the complexes formed upon aggregation of hydrogen molecules on this substrate. Accurate force fields based on high level electronic structure calculations have been built using a rigid rotor model for the hydrogen molecules as well as a orresponding pseudo-atom approximation, aimed to pursue larger compounds where a simpler treatment could be helpful. Structural and energy features of the hydrogen adsorption have been then analyzed by means of quantum Monte Carlo methods. A large stabilization of the adsorption energy is found for up to four H2 molecules attached to the alkali atom, in agreement with conclusions reached from previous studies on smaller Na-decorated PAHs. Adsorption patterns are examined in detail as the number of attached molecules is increased, comparing with results on smaller substrates and analyzing the effects of rotational orientation by contrasting the rigid rotor vs. pseudo-atom approaches.