Aerosol drug delivery is a viable option for treating diseased airways, but airway obstructions associated with diseases such as cystic fibrosis cause non-uniform drug distribution and limit efficacy. Marangoni stresses produced by surfactant addition to aerosol formulations may enhance delivery uniformity by post-deposition spreading of medications over the airway surface, improving access to poorly ventilated regions. We examine the roles of different variables affecting the maximum post-deposition spreading of a dye (drug mimic). Entangled aqueous solutions of either poly(acrylamide) (PA) or porcine gastric mucin (PGM) serve as airway surface liquid (ASL) mimicking subphases for in vitro models of aerosol deposition. Measured aerosol deposition fluxes indicate that the experimental delivery conditions are representative of aerosol delivery to the conducting airways. Post-deposition spreading beyond the locale of direct aerosol deposition is tracked by fluorescence microscopy. Aqueous aerosols formulated with either nonionic surfactant (tyloxapol) or fluorosurfactant (FS-3100) are compared with surfactant-free control aerosols. Significant enhancement of post-deposition spreading is observed with surfactant solutions relative to surfactant-free control solutions, provided the surfactant solution surface tension is less than that of the subphase. Amongst the variables considered--surfactant concentration, aerosol flow-rate, total deposited volume, time of delivery, and total deposited surfactant mass--surfactant mass is the primary predictor of maximum spread distance. This dependence is also observed for solutions deposited as a single, microliter-scale drop with a volume comparable to the total volume of deposited aerosol. Marangoni stress-assisted spreading after surfactant-laden aerosol deposition at high fluxes on a complex fluid subphase is capable of driving aerosol contents over significantly greater distances compared to surfactant-free controls. Total delivered surfactant mass is the primary determinant of the extent of spreading, suggesting a great potential to extend the reach of aerosolized medication in partially obstructed airways via a purely physical mechanism.