Fine dexterous manipulation requires reactive control based on rich sensing of manipulator-object interactions. Tactile sensing arrays provide rich contact information across the manipulator's surface. However their implementation faces two main challenges: accurate force estimation across complex surfaces like robotic hands, and integration of these estimates into reactive control loops. We present a data-efficient calibration method that enables rapid, full-array force estimation across varying geometries, providing online feedback that accounts for non-linearities and deformation effects. Our force estimation model serves as feedback in an online closed-loop control system for interaction force tracking. The accuracy of our estimates is independently validated against measurements from a calibrated force-torque sensor. Using the Allegro Hand equipped with Xela uSkin sensors, we demonstrate precise force application through an admittance control loop running at 100Hz, achieving up to 0.12+/-0.08 [N] error margin-results that show promising potential for dexterous manipulation.