Ultraviolet spectra of protoplanetary disks trace distributions of warm gas at radii where rocky planets form. We combine HST-COS observations of H2 and CO emission from 12 classical T Tauri stars to more extensively map inner disk surface layers, where gas temperature distributions allow radially stratified fluorescence from the two species. We calculate empirical emitting radii for each species under the assumption that the line widths are entirely set by Keplerian broadening, demonstrating that the CO fluorescence originates further from the stars (r ~ 20 AU) than the H2 (r ~ 0.8 AU). This is supported by 2-D radiative transfer models, which show that the peak and outer radii of the CO flux distributions generally extend further into the outer disk than the H2. These results also indicate that additional sources of LyA photons remain unaccounted for, requiring more complex models to fully reproduce the molecular gas emission. As a first step, we confirm that the morphologies of the UV-CO bands and LyA radiation fields are significantly correlated and discover that both trace the degree of dust disk evolution. The UV tracers appear to follow the same sequence of disk evolution as forbidden line emission from jets and winds, as the observed LyA profiles transition between dominant red wing and dominant blue wing shapes when the high-velocity optical emission disappears. Our results suggest a scenario where UV radiation fields, disk winds and jets, and molecular gas evolve in harmony with the dust disks throughout their lifetimes.