We present the results of hydrodynamic simulations examining migration and growth of planets embedded in self-gravitating circumbinary discs. The binary star parameters are chosen to mimic those of the Kepler-16, -34 and -35 systems; the aim of this study is to examine the role of disc mass in determining the stopping locations of migrating planets at the edge of the cavity created by the central binary. Disc self-gravity can cause significant shrinkage of the cavity for disc masses in excess of 5--10 $\times$ the minimum mass solar nebula model. Planets forming early in the disc lifetime can migrate through the disc and stall at locations closer to the central star than is normally the case for lower mass discs, resulting in closer agreement between simulated and observed orbital architecture. The presence of a planet orbiting in the cavity of a massive disc can prevent the cavity size from expanding to the size of a lower mass disc. As the disc mass reduces over long time scales, this indicates that circumbinary planet systems retain memory of their initial conditions. Our simulations produce planetary orbits in good agreement with Kepler-16b without the need for self-gravity; Kepler-34 analogue systems produce wide and highly eccentric cavities, and self-gravity improves the agreement between simulations and data. Kepler-35b is more difficult to explain in detail due to it's relatively low mass, which results in the simulated stopping location being at a larger radius than that observed.