The outer giant planets, Uranus and Neptune, pose a challenge to theories of planet formation. They exist in a region of the solar system where long dynamical timescales and a low primordial density of material would have conspired to make the formation of such large bodies (~15 and 17 times as massive as Earth, respectively) very difficult. Previously, we proposed a model that addressed this problem: Instead of forming in the trans-Saturnian region, Uranus and Neptune underwent most of their growth among proto-Jupiter and proto-Saturn, were scattered outward when Jupiter acquired its massive gas envelope, and subsequently evolved toward their present orbits. We present the results of additional numerical simulations, which further demonstrate that the model readily produces analogs to our solar system for a wide range of initial conditions. We also find that this mechanism may partly account for the high orbital inclinations observed in the Kuiper belt.