We demonstrate a novel closed-loop approach for high-precision co-alignment of laser beams in an actively phase-locked, coherently combined fiber laser array. The approach ensures interferometric precision by optically transducing beam-to-beam pointing errors into phase errors on a single detector, which are subsequently nulled by duplication of closed-loop phasing controls. Using this approach, beams from five coherent fiber tips were simultaneously phase-locked and position-locked with sub-micron accuracy. Spatial filtering of the sensed light is shown to extend the control range over multiple beam diameters by recovering spatial coherence despite the lack of far-field beam overlap.