We present results of our recently expanded static corrugation model (SCM) approach that included the relevant surface temperature effects, applied to the dissociative chemisorption reaction of H2 on a Cu(111) surface. The reaction and rovibrationally elastic scattering probabilities that we obtain at a quantum dynamical (QD) level, as an average of many statically distorted surface configurations, show great agreement with those of a dynamic surface model, which reinforces the validity of the sudden approximation inherent to the SCM. We further investigate several simple methods of binning the final rovibrational state of quasi-classical dynamics simulations, to find those best suited to reproduce the QD results for our system. Finally, we show that the SCM obtained results reproduce experimental dissociation curves very well, when the uncertainty in experimental saturation values is taken into account. Some indication of a slow channel, so far only observed in experiment, can also be found at low incidence energies, although more rigorous QD simulations are required to reduce the noise inherent to our propagation methods.