Precise grasp force regulation in tendon-driven surgical instruments is fundamentally limited by nonlinear coupling between motor dynamics, transmission compliance, friction, and distal mechanics. Existing solutions typically rely on distal force sensing or analytical compensation, increasing hardware complexity or degrading performance under dynamic motion. We present a sensorless control framework that combines physics-consistent modeling and hybrid reinforcement learning to achieve high-precision distal force regulation in a proximally actuated surgical end-effector. We develop a first-principles digital twin of the da Vinci Xi grasping mechanism that captures coupled electrical, transmission, and jaw dynamics within a unified differential-algebraic formulation. To safely learn control policies in this stiff and highly nonlinear system, we introduce a three-stage pipeline:(i)a receding-horizon CMA-ES oracle that generates dynamically feasible expert trajectories,(ii)fully offline policy learning via Implicit Q-Learning to ensure stable initialization without unsafe exploration, and (iii)online refinement using TD3 for adaptation to on-policy dynamics. The resulting policy directly maps proximal measurements to motor voltages and requires no distal sensing. In simulation, the controller maintains grasp force within 1% of the desired reference during multi-harmonic jaw motion. Hardware experiments demonstrate average force errors below 4% across diverse trajectories, validating sim-to-real transfer. The learned policy contains approximately 71k param and executes at kH rates, enabling real-time deployment. These results demonstrate that high-fidelity modeling combined with structured offline-online RL can recover precise distal force behavior without additional sensing, offering a scalable and mechanically compatible solution for surgical robotic manipulation.