An initial three-station version of the Event Horizon Telescope, a millimeter-wavelength very-long baseline interferometer, has observed Sagittarius A* (Sgr A*) repeatedly from 2007 to 2013, resulting in the measurement of a variety of interferometric quantities. Of particular importance is that there is now a large set of closure phases measured over a number of independent observing epochs. We analyze these observations within the context of a realization of semi-analytic radiatively inefficient disk models, implicated by the low luminosity of Sgr A*. We find a broad consistency among the various observing epochs and between different interferometric data types, with the latter providing significant support for this class of model of Sgr A*. The new data significantly tighten existing constraints on the spin magnitude and its orientation within this model context, finding a spin magnitude of a={0.10}-0.10-0.10 0.30 0.56, an inclination with respect to the line of sight of ? ={60^\circ }-{8^\circ -{13}^\circ } {5^\circ {10}^\circ }, and a position angle of ? ={156^\circ }-{17^\circ -{27}^\circ } {10^\circ {14}^\circ } east of north. These are in good agreement with previous analyses. Notably, the previous 180° degeneracy in the position angle has now been conclusively broken by the inclusion of the closure-phase measurements. A reflection degeneracy in the inclination remains, permitting two localizations of the spin vector orientation, one of which is in agreement with the orbital angular momentum of the infrared gas cloud G2 and the clockwise disk of young stars. This may support a relationship between Sgr A*'s accretion flow and these larger-scale features.
