In Paper I of this series, we show that transient lunar phenomena (TLPs) correlate with lunar outgassing, geographically, based on surface radon release episodes versus the visual record of telescopic observers (the later prone to major systematic biases of unspecified nature, which we were able to constrain in Paper I). In Paper II we calculate some of the basic predictions that this insight implies, in terms of outgassing/regolith interactions. In this paper we propose a path forward, in which current and forthcoming technology provide a more controlled and sensitive probe of lunar outgassing. Many of these techniques are currently being realized for the first time.Given the optical transient/outgassing connection, progress can be made by Earth-based remote sensing, and we suggest several programs of imaging, spectroscopy and combinations thereof. However, as found in Paper II, many aspects of lunar outgassing seem likely to be covert in nature. TLPs betray some outgassing, but not all outgassing produces TLPs. Some outgassing may never appear at the surface, but remain trapped in the regolith.As well as passive remote sensing, we also suggest more intrusive techniques, from radar mapping to in-situ probes. Understanding these volatiles seems promising in terms of their exploitation as a resource for human presence on the Moon and beyond, and offers an interesting scientific goal in its own right. This paper reads, therefore, as a series of proposed techniques, some in practice, some which might be soon, and some requiring significant future investment (some of which may prove unwise pending results from predecessor investigations). These point towards enhancement of our knowledge of lunar outgassing, its relation to other lunar processes, and an increase in our understanding of how volatiles are involved in the evolution of the Moon. We are compelled to emphasize certain ground-based observations in time for the flight of SELENE, LRO and other robotic missions, and others before extensive