Recently, the DOA (Direction Of Arrival) estimation of an acoustic wavefront has been considered in a setting where the inference task is performed by a Wireless Sensor Network (WSN) made of isotropic (hence individually useless) sensors. The WSN was designed according to the SENMA architecture with a Mobile Agent (MA) that successively queries the sensors lying inside its field of view. In this paper the ideal assumption previously made that the visibility of individual sensors is governed by deterministic laws is relaxed; this yields, interestingly, simpler analytical formulas. Both fast/simple and optimal DOA-estimation schemes are proposed, and an optimization of the MA's observation management is also carried out, with the surprising finding that the MA ought to orient itself at an oblique angle to the expected DOA, rather than directly toward it. The extension to multiple sources is also considered; intriguingly, per-source DOA accuracy is higher when there is more than one...