The Airy wanderer line ensembles are infinite-parameter generalizations of the classical Airy line ensemble that arise naturally as scaling limits of inhomogeneous (spiked) models in the Kardar-Parisi-Zhang universality class. In this paper, we establish several structural properties of these ensembles. Our results show their laws depend continuously on the parameters, which encode the asymptotic slopes of the ensemble's curves near positive and negative infinity. We further prove that these ensembles admit multiple monotone couplings with respect to their parameters. Finally, we show that the Airy wanderer line ensembles are extreme points in the space of all Brownian Gibbsian line ensembles on the real line.