Stars between two and three solar masses rotate rapidly on the main sequence, and the detection of slow core and surface rotation in the core-helium burning phase for these stars places strong constraints on their angular momentum transport and loss. From a detailed asteroseismic study of the mixed-dipole mode pattern in a carefully selected, representative sample of stars, we find that slow core rotation rates in the range reported by prior studies are a general phenomenon and not a selection effect. We show that the core rotation rates of these stars decline strongly with decreasing surface gravity during the core He-burning phase. We argue that this is a model-independent indication of significant rapid angular momentum transport between the cores and envelopes of these stars. We see a significant range in core rotation rates at all surface gravities, with little evidence for a convergence toward a uniform value. We demonstrate using evolutionary models that measured surface rotation periods are a biased tracer of the true surface rotation distribution, and we argue for using stellar models for interpreting the contrast between core and surface rotation rates. The core rotation rates we measure do not have a strong mass or metallicity dependence. We argue that the emerging data strongly favor a model where angular momentum transport is much more efficient during the core He-burning phase than in the shell-burning phases that precede and follow it.