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We present the design of a low-complexity air interface for the uplink in Low Power Wide Area Networks (LPWANs) based on a recently published Differential Spatial Modulation scheme for two transmit antennas achieving full transmit diversity (FD-DSM). Extending the authors' work, we derive an optimized assignment from bits to space-time matrices comparable to Gray coding, which improves the bit error rate by up to 1 dB. Furthermore, FD-DSM's superiority over single-antenna differential PSK schemes as used in current LPWAN technologies is evaluated in extensive simulations and confirmed in uncoded and coded scenarios, where a convolutional code with soft-input Viterbi decoding is employed. It is shown that existing systems are outperformed by at least 5 dB for packet error rates below 1%. Our system utilizes the DSSS technique to achieve the enormous processing gains required to enable links over many kilometers. We propose the insertion of time gaps between chip sequences to allow for the rise and fall time of conventional, spectrally-efficient pulse shaping filters and to thus facilitate antenna switching without spectral broadening, a challenging issue in Spatial Modulation (SM) systems. The resulting rate loss is negligible but allows the realization of practical SM systems with the theoretical minimum of a single RF chain.