Electrical effects can impart a cross-stream component to drop motion in a pressure-driven flow, due to either an asymmetric charge distribution or shape deformation. However, surfactant-mediated alterations in such migration characteristics remain unexplored. By accounting for three-dimensionality in the drop motion, we analytically demonstrate here a non-trivial switching of drop migration with the aid of a surfactant coating on its surface. We establish this phenomenon as controllable by exploiting an interconnected interplay between the hydrodynamic stress, electrical stress and Marangoni stress, manifested so as to achieve a net interfacial force balance. Our results reveal that under different combinations of electrical conductivity and permittivity ratios, the relative strength of the electric stress with respect to the hydrodynamic stress, the applied electric field direction and the surfactants alter the longitudinal and cross-stream velocity components of the droplets differently. The effect of drop deformation on its speed is found to be altered with the increased sensitivity of the surface tension to the surfactant concentration, depending on the competing effects of the electrohydrodynamic flow modification and the tip stretching phenomenon. Further, with a suitable choice of electrical property ratios, the Marangoni effects can be exploited to direct the drop in reaching a final transverse position towards or away from the channel centreline. These results may turn out to be of immense consequence in providing an insight to the underlying complex physical mechanisms dictating an intricate control on the drop motion in different directions.