The recently proposed Grand Tack model (Walsh et al., 2011) couples the gas-driven migration of giant planets to the accretion of terrestrial planets. In this model the first inward and then outward migration of Jupiter and Saturn creates a truncated disk of embryos and planetesimals, the subsequent evolution of which eventually broadly reproduces the orbital and mass distributions of the terrestrial planets, including a small Mars. Here we show that the Grand Tack model for the formation of the terrestrial planets can also match important accretion constraints including the time and mass of the last giant (i.e. Moon forming) impact on the Earth, the mass of the late veneer, and the rapid accretion of Mars. Expanding from Walsh et al. (2011), we explore a variety of oligarchic growth regime configurations. We adjust the individual mass of the initial embryos and the ratio of total masses in embryos and planetesimals. The individual embryo mass is diagnostic of the efficiency of the oligarchic growth process and/or its duration before being interrupted by the migration of Jupiter. We discover that more massive embryos can explain the rapid accretion timescale of Mars. The ratio of total masses in embryos and planetesimals is a reflection of the severity of collisional grinding during the oligarchic growth phase and its duration before interruption. An increased embryo to planetesimal total mass ratio creates Solar System analogs with evolution histories more similar to our own, including the timing of the last giant impact on Earth analogs and the small mass of the late veneer. Adjusting these parameters weakly effects on the final orbit and mass distributions of the simulated systems. After 150 million years of evolution, most are Solar System analogs with 4 or 5 planets that capture the mass-orbit relationship of the real terrestrial planets. The major drawback of these simulations is that the synthetic Mercury is typically too massive and too far from the Sun. To solve this problem, we will present results from simulations where the initial embryo mass increases with semi-major axis and we will explore the possibility that a small embryo was scattered inwards off the inner edge of the disk during early times.