We study the dynamical evolution of the putative gas clouds G1 and G2 recently discovered in the Galactic center. Following earlier studies suggesting that these two clouds are part of a larger gas streamer, we combine their orbits into a single trajectory. Since the gas clouds experience a drag force from background gas, this trajectory is not exactly Keplerian. By assuming the G1 and G2 clouds trace this trajectory, we fit for the drag force they experience and thus extract information about the accretion flow at a distance of thousands of Schwarzschild radii from the black hole. This range of radii is important for theories of black hole accretion, but is currently unconstrained by observations. In this paper we extend our previous work by accounting for radial forces due to possible inflow or outflow of the background gas. Such radial forces drive precession in the orbital plane, allowing a slightly better fit to the G1 and G2 data. This precession delays the pericenter passage of G2 by 4-5 months relative to estimates derived from a Keplerian orbital fit; if it proves possible to identify the pericenter time observationally, this enables an immediate test of whether G1 and G2 are gas clouds part of a larger gas streamer. If G2 is indeed a gas cloud, its closest approach likely occurred in late summer 2014, after many of the observing campaigns monitoring G2s anticipated pericenter passage ended. We discuss how this affects interpretation of the G2 observations.