The combustion of porous energetic materials under confinement is generally characterized by a relatively rapid increase in the flame-propagation speed as the pressure difference, or overpressure, between the burned gases in the product region and the unburned gases deep within the pores of the unburned solid increases. The structure of the deflagration wave during this transition from conductive to convective burning is likely to correspond to a previously identified intrusive regime associated with higher overpressures. In this intrusive limit, the distributed gas-phase reactions proceed in the vicinity of the solid/gas interface, where surface reactions representing sublimation and pyrolysis occur. In this merged-flame regime, gaseous combustion can then either be confined to the purely gas-phase region beyond the solid surface or, depending on a number of factors, can penetrate inside the unburned porous material. A large-activation-energy analysis of the latter scenario is presented in this work to investigate the effects of gas-phase reaction permeation on the structure and propagation speed of quasi-steady deflagrations in confined porous propellants. The results of the current study are compared to the corresponding results that are obtained when, in the same intrusive regime, the gas flame is assumed not to penetrate into the subsurface region. It is demonstrated that the burning rate derived in the current scenario exhibits a higher sensitivity to increasing overpressure, because the heat release from gas-phase reactions within the porous solid permits additional preheating of the material.