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We present a study of the Galactic supernova remnant (SNR) G292.0+1.8, a classic example of a core-collapse SNR that contains oxygen-rich ejecta, circumstellar material, a rapidly moving pulsar, and a pulsar wind nebula (PWN). We use hydrodynamic simulations of the remnant evolution to show that the SNR reverse shock is interacting with the PWN and has most likely shocked the majority of supernova ejecta. In our models, such a scenario requires a total ejecta mass of $\lesssim 3\: \rm M_{\odot}$ and implies that there is no significant quantity of cold ejecta in the interior of the reverse shock. In light of these results, we compare the estimated elemental masses and abundance ratios in the reverse-shocked ejecta to nucleosynthesis models and find that they are consistent with a progenitor star with an initial mass of 12-16 $\: \rm M_{\odot}$. We conclude that the progenitor of G292.0+1.8 was likely a relatively low mass star that experienced significant mass loss through a binary interaction and would have produced a stripped-envelope supernova explosion. We also argue that the region known as the "spur" in G292.0+1.8 arises as a result of the pulsar's motion through the supernova ejecta and that its dynamical properties may suggest a line-of-sight component to the pulsar's velocity, leading to a total space velocity of $\sim 600\: \rm km\:s^{-1}$ and implying a significant natal kick. Finally, we discuss binary mass loss scenarios relevant to G292.0+1.8 and their implications for the binary companion properties and future searches.