Tracking multiple prioritized tasks simultaneously with redundant robots have been investigated extensively over the last decades. Recent research focuses on combining advantages from both classical soft and strict prioritization schemes which is non-trivial. Among the proposed methods to tackle this issue, Generalized Hierarchical Control (GHC) seems to have a reasonable performance, however, it does not include a weighting matrix in the computation of the nullspace projection operator and hence cannot construct dynamically-consistent stack-of-tasks hierarchies as a special case. We extend GHC by adding dynamic-consistency to the control scheme and refer to it as DynGHC. The extension is also advantageous when choosing non-strict priorities because inertia coupling between tasks is reduced. DynGHC allows to smoothly rearrange priorities which is important for robots acting in dynamically changing contexts. Comparative simulations with a 4 DOF planar manipulator and a KUKA LWR validate our approach. Matlab and C++ source code is made available.