Recently, Einsiedler and the authors provided a bound in terms of escape of mass for the amount by which upper-semicontinuity for metric entropy fails for diagonal flows on homogeneous spaces $\unicode[STIX]{x1D6E4}\setminus G$ , where $G$ is any connected semisimple Lie group of real rank one with finite center, and $\unicode[STIX]{x1D6E4}$ is any non-uniform lattice in $G$ . We show that this bound is sharp, and apply the methods used to establish bounds for the Hausdorff dimension of the set of points that diverge on average.