In late 2014, the solar wind dynamic pressure increased by ~50% over a relatively short time (~6 months). In early 2017, the Interstellar Boundary Explorer (IBEX) observed an increase in heliospheric energetic neutral atom (ENA) fluxes from directions near the front of the heliosphere. These enhanced ENA emissions resulted from the increase in SW pressure propagating through the inner heliosheath (IHS), affecting the IHS plasma pressure and emission of ~keV ENA fluxes. We expand on the analysis by McComas et al. on the effects of this pressure change on ENA fluxes observed at 1 au using a three-dimensional, time-dependent simulation of the heliosphere. The pressure front has likely already crossed the termination shock (TS) in all directions, but ENA fluxes observed at 1 au will change over the coming years, as the TS, heliopause, and IHS plasma pressure continue to change in response to the SW pressure increase. Taken in isolation, the pressure front creates a "ring" of increasing ENA fluxes projected in the sky that expands in angular radius over time, as a function of the distances to the heliosphere boundaries and the ENA propagation speed. By tracking the position of this ring over time in our simulation, we demonstrate a method for estimating the distances to the TS, heliopause, and ENA source region that can be applied to IBEX data. This will require IBEX observations at 4.3 keV up through ~2020, and longer times at lower ENA energies, in order to observe significant changes from the heliotail.