Direct laser acceleration leveraging transverse fields promises unparalleled gradients exceeding 1 TeV/m yet is fundamentally constrained by phase slippage, which limits interaction length and final energy gain. Here, we overcome this dephasing limitation by employing a pulse-front-tilted (PFT) laser interacting with a plasma grating. This configuration ensures sustained phase matching, facilitating extended acceleration and stable near-field confinement. Uniquely, this structure functions as a phase-selective sieve that generates dense electron bunches with durations of hundreds of attoseconds. Particle-in-cell simulations demonstrate that a 61 J laser pulse yields an 11 pC beam with energies surpassing 10 GeV at gradients of approximately 2 TeV/m. Derived for an idealized dephasingless regime, linear scaling laws predict that 1 kJ pulses can drive beams to 200 GeV. These findings present a promising pathway toward on-chip TeV-scale accelerators and attosecond sources, with potential applications for high-energy colliders, ultrafast electron imaging, and advanced light sources.