Using an 800 nm, 45 fs pulse-front-tilted laser we demonstrate a record 315 keV energy gain in a dual grating dielectric laser accelerator (DLA) and average accelerating gradients of 560 MV/m over 0.5 mm. These results open a new regime in DLA characterized by significant evolution of the beam distribution in the longitudinal phase space, corresponding to >1/4 of a synchrotron oscillation. By tilting the laser wavefront we control the resonant velocity of the DLA and observe a net energy gain, indicating that a tapered optical phase could be used to achieve very high energy gain.