The hydrogen ionization and dissociation front around an ultraviolet radiation source should merge when the ratio of ionizing photon flux to gas density is sufficiently low and the spectrum is sufficiently hard. This regime is particularly relevant to the molecular knots that are commonly found in evolved planetary nebulae, such as the Helix Nebula, where traditional models of photodissociation regions have proved unable to explain the high observed luminosity in H₂ lines. In this paper we present results for the structure and steady state dynamics of such advection-dominated merged fronts, calculated using the Cloudy plasma/molecular physics code. We find that the principal destruction processes for H₂ are photoionization by extreme ultraviolet radiation and charge-exchange reactions with protons, both of which form H₂⁺, which rapidly combines with free electrons to undergo dissociative recombination. Advection moves the dissociation front to lower column densities than in the static case, which vastly increases the heating in the partially molecular gas due to photoionization of He⁰, H₂, and H⁰. This causes a significant fraction of the incident bolometric flux to be reradiated as thermally excited infrared H₂ lines, with the lower excitation pure rotational lines arising in 1000 K gas and higher excitation H₂ lines arising in 2000 K gas, as is required to explain the H₂ spectrum of the Helix cometary knots.