We study the electrically driven spreading of dielectric liquid films in wedge-shaped gaps across which a potential difference is applied. Our experiments are in a little-studied regime where, throughout the dynamics, the electrical relaxation time is long compared to the time for charge to be convected by the fluid motion. We observe that at a critical normal electric field the hump-shaped leading edge undergoes an instability in the form of a single Taylor cone and periodic jetting ensues, after which traveling waves occur along the trailing thin film. We propose a convection-dominated mechanism for charge transport to describe the observed dynamics and rationalize the viscosity dependence of the self-excited dynamics.