The no-insulation (NI) approach to winding (RE)Ba2Cu3Ox (REBCO) high temperature superconductor solenoids has shown significant promise for maximizing the efficient usage of conductor while providing self-protecting operation. Self-protection in a NI coil, however, does not diminish the likelihood that a recoverable quench occurs. During a disturbance resulting in a recoverable quench, owing to the low turn-to-turn contact resistance, transport current bypasses the normal zone by flowing directly from the current input lead to the output lead, leading to a near total loss of the azimuthal current responsible for magnetic field generation. The consequences are twofold. First, a long recovery process is needed to recharge the coil to full operational functionality. Second, a fast magnetic field transient is created due to the sudden drop in magnetic field in the quenching coil. The latter could induce a global inductive quench propagation in other coils of a multi-coil NI magnet, increasing the likelihood of quenching and accelerating the depletion of useful current in other coils, lengthening the post-quench recovery process. Here a novel graded-resistance method is proposed to tackle the mentioned problems while maintaining the superior thermal stability and self-protecting capability of NI magnets. Through computational modeling and analysis on a hybrid multiphysics model, patterned resistive-conductive layers are inserted between selected turn-to-turn contacts to contain hot-spot heat propagation while maintaining the turn-wise current sharing required for self-protection, resulting in faster post-quench recovery and reduced magnetic field transient. Effectiveness of the method is studied at 4.2 and 77 K. Through the proposed method, REBCO magnets with high current density, high thermal stability, low likelihood of quenching, and rapid, passive recovery emerge with high operational reliability and availability.