Direct-to-device (D2D) satellite connectivity, an exemplar of non-terrestrial network (NTN) integration with 5G and forthcoming 6G mobile ecosystem, is enjoying rapidly growing prominence. Delivering space-enabled broadband connectivity to smartphones, with their low-power, omnidirectional antennas, requires multitude of technological advancements. One innovation exploits distributed satellite systems using swarms of small regenerative satellites in low-Earth orbit (LEO) that synthesize multiple steerable beams. Another advancement optimizes efficiency of the already scarce radio-frequency (RF) spectrum with full frequency reuse, unfortunately intensifying intrabeam interference. This paper develops novel methodology for unified interference mitigation, comprised of selective precoder and high-performance receiver. Precoder is based on maximizing signal-to-leakage-and-noise ratio (SLNR), made selective about which subset of interference to leave unmitigated. It has low complexity, implemented in two stages to reduce computational requirements and alleviate user-scheduling constraints. High-performance receiver jointly processes signal and dominant interference, building on divide-and-conquer (DAC) paradigm to synergize with selective precoding. It has low complexity with computational load that does not grow exponentially with the number of dominant interferers. Extensive simulations reveal that unified interference mitigation significantly surpasses state-of-the-art schemes in sum-rate throughput, outage probability, and block error rate, also under scenarios of synchronization errors and imperfect channel state information at the transmitter (CSIT).