The processing and application properties of hot-melt pressure-sensitive adhesives (HMPSA) are governed, to a large extent, by their rheological properties. Coating of the HMPSA is performed at high temperatures in the molten state. At room temperature, the adhesive satisfies the Dahlquist criterion and, consequently, has permanent tack. We have particularly studied the full formulations based on triblock and diblock copolymers, and also those based on newly designed molecules, such as tetrablock or radial copolymers. We have demonstrated in the previous articles of this series that, for these systems, the volume fraction of the free polyisoprene is the most important parameter that drives the tack performances by controlling the level of the secondary elastic plateau modulus observed in the low-frequency range. To improve the end-user properties, we have increased the diblock content in the blends. We describe here the dynamic mechanical properties, at room temperature, of the pure copolymer blends (i.e., without addition of a tackifying resin) and the full HMPSA formulations. We focus particularly in this article on blends that contain a high diblock content. The effect of the morphology of the diblock copolymer on the rheological behavior of the adhesive is discussed in detail. Finally, we propose a model, based on molecular dynamics concepts, which describes the rheological behavior in a very wide range of frequencies for all copolymers and full formulations of the study.