Cesium-137 is a major byproduct of nuclear energy generation and is environmentally threatening due to its long half-life and affinity for naturally occurring micaceous clays. Recent experimental observations of illite and phlogopite mica indicate that Cs+ is capable of exchanging with K+ bound in the anhydrous interlayers of layered silicates, forming sharp exchange fronts, leading to interstratification of Cs- and K-illite. We present here a coarse-grained (CG) model of the anhydrous illite interlayer developed using iterative Boltzmann inversion that qualitatively and quantitatively reproduces features of a previously proposed feedback mechanism of ion exchange. The CG model represents a 70-fold speedup over all-atom models of clay systems and predicts interlayer expansion for K-illite near ion exchange fronts. Contrary to the longstanding theory that ion exchange in a neighboring layer increases the binding of K in lattice counterion sites leading to interstratification, we find that the presence of neighboring exchanged layers leads to short-range structural relaxations that increase basal spacing and decrease cohesion of the neighboring K-illite layers. We also provide evidence that the formation of alternating Cs- and K-illite interlayers (i.e., ordered interstratification) is both thermodynamically and mechanically favorable compared to exchange in adjacent interlayers.