The decomposition of neurophysiological recordings into their constituent neural sources is of major importance to a diverse range of neuroscientific fields and neuroengineering applications. The advent of high density electrode probes and arrays has driven a major need for novel semi-automated and automated blind source separation methodologies that take advantage of the increased spatial resolution and coverage these new devices offer. Independent component analysis (ICA) offers a principled theoretical framework for such algorithms, but implementation inefficiencies often drive poor performance in practice, particularly for sparse sources. Here we observe that the use of a single non-linear optimization function to identify spiking sources with ICA often has a detrimental effect that precludes the recovery and correct separation of all spiking sources in the signal. We go on to propose a projection-pursuit ICA algorithm designed specifically for spiking sources, which uses a particle swarm methodology to adaptively traverse a polynomial family of non-linearities approximating the asymmetric cumulants of the sources. We robustly prove state-of-the-art decomposition performance on recordings from high density intramuscular probes and demonstrate how the particle swarm quickly finds optimal contrast non-linearities across a range of neurophysiological datasets.