M-ary Aggregate Spread Pulse Modulation (M-ASPM) is a recently introduced physical layer (PHY) modulation technique that is well suited for use in low-power wide-area networks (LPWANs). Notably, M-ASPM combines high energy-per-bit efficiency, robustness, resistance to interference, and a number of other favorable technical characteristics, with the spread-spectrum ability to maintain the capacity of an uplink-focused network while extending its range. However, while the essential tools for detection and synchronization of pulsed spread-spectrum waveforms in general, and the M-ASPM signals in particular, have been previously provided, a practical framework for combining the detection, synchronization, and decoding of an M-ASPM packet has not been yet suggested. In this paper, we outline such a framework, and describe a prototype algorithm for its implementation. This implementation can be subsequently adapted, under given technical constraints, to specific practical complications such as, for example, significant delay spreads, external technogenic interference, or co-channel and inter-channel collisions. In addition to low latency and computational complexity, the main requirement for this prototype algorithm is that the signal quality remains effectively invariant, for a given path loss, and for a wide range of the data rates, payload sizes, lengths of pulse shaping filters (PSFs), and pulse duty cycles, for a relatively large mismatch in the frequency of the local oscillators (LOs) in the transmitter (TX) and the receiver (RX), and for the TX and RX motions at relatively high speeds. Further, this needs to be achieved without any feedback communications between the TX and RX, any hardware or software changes in the TX, and any hardware adjustments in the RX (e.g., in the LO~frequency or sampling time offsets).