Ion-Stark line broadening is a key density diagnostic for hot dense plasmas relevant to inertial fusion and astrophysics. It is caused by interactions of a radiating ion with nearby perturbing ions, whose electric microfields lead to changes in bound-bound transition energies. Ion-Stark broadening becomes increasingly difficult to compute for complex, many-electron ions with myriad transitions. In this paper, we propose a simplified approach to ion-Stark broadening based on self-consistent ion distributions and electronic structure from an average-atom model. We find that this approach reproduces the line shape predictions of one traditional method for high-n K-shell emission lines in aluminum ions with accuracy sufficient for density diagnostics in thermal plasmas with equal ion and electron temperatures. We expect that this approach can be extended to provide a reasonable picture of ion-Stark broadening in many-electron ions, enabling rapid calculations of line profiles in complex spectra.