The microscopic diffusion of CO on stepped Pt(111) crystal surfaces has been investigated with pulsed molecular beam-time-resolved surface infrared methods. Following a rapid exposure to CO, we record the time evolution of the CO surface vibrational spectra as the CO diffuse from the initial random distribution to the thermodynamically favored step sites. The data are simulated with a model that describes the kinetics of diffusion across the terraces, as well as the filling of step sites. We critically evaluate this model and the general experimental approach by extending our previous measurements of CO diffusion on Pt(28(111)-(11BAR0)) to a surface with higher step density, Pt(12(111)-(11BAR0)), with varying coverages. The model describes both sets of data with the same parameters, confirming the original determination of the diffusion barrier (DELTA-E(T)) and prefactor (A(T)) for microscopic surface hopping of CO/Pt(111). This further provides a quantitative means to estimate systematic errors. We report DELTA-E(T) = 4.0 +/- 0.7 kcal/mol and A(T) = 10(9.2) s-1, with minimum and maximum possible values of 10(7.0) and 10(10.4) s-1 for A(T).