Time-resolved infrared-ultraviolet double resonance (IR-UV DR) spectroscopy provides a distinctive way to examine collision-induced state-to-state energy transfer between rotational J-levels in vibrational manifolds of small polyatomic molecules, such as acetylene (C₂H₂) in its electronic ground state "X". We consider the 4v[CH] rovibrational manifold of C₂H₂ at ~12 700 cm⁻¹, where the principal source of IR-brightness is the (v₁ + 3v₃) or (1 0 3 0 0)⁰ ∑⁺u vibrational combination level. In this highly congested manifold, anharmonic, l-resonance, and Coriolis couplings affect the J-levels of interest, implicating them in a complicated variety of intramolecular dynamics. Previous papers of this series have reported several seemingly anomalous J-resolved phenomena induced by collisions in C₂H₂ gas at room temperature with pressures and IR-UV pump-probe delay intervals corresponding to remarkably high Lennard- Jones collisional efficiencies 'P': odd-∆J rotational energy transfer (10⁻³ < 'P' < 0.1), in addition to regular even-∆J transfer ('P' ≈ 0.3 for typical ∣∆J∣ = 2 transfer); particular rovibrational “gateway” channels, such as Via (v₁ + 3v₃) ∑⁺u J = 12 (with 'P' as high as ~0.1); an apparently ubiquitous collision-induced quasi-continuous background (10⁻³ < 'P' < 0.1) that accounts for much of the observed collision-induced odd-∆J satellite structure. These phenomena have been characterized by means of systematic IR-UV DR kinetic measurements, with IR pump and UV probe wavelengths and sample pressure fixed while the IR-UV pump-probe delay is scanned. In this paper, a detailed masterequation model is constructed to provide a satisfactory phenomenological fit to the IR-UV DR kinetic data, thereby offering mechanistic insight. This model includes collision-induced energy transfer between discrete rovibrational levels in an IR-bright manifold V and a quasi-continuous bath B, mediated by a J-specific gateway manifold G.