Measurements and analyses [J. P. Apruzese et al., Phys. Plasmas 12, 012705 (2005)] of Al and MgK-shell lines from tracer layers symmetrically embedded in cylindrical dynamic-Hohlraum (DH) targets, driven by two nested tungsten-wire arrays in a z pinch, suggest that the radiation temperatures near either end of top or bottom radiation exit holes (REHs) of the DHs are similar. Moreover, the measured radii inferred for the shock developed within the targets converge towards the z axis symmetrically when viewed simultaneously through either end of the Hohlraums. These two results support the earlier observation [T. W. L. Sanford et al., Phys. Plasmas 12, 022701 (2005)] that the anticorrelation of the axial power with the magnitude of tungsten-wire material flowing near (or across) the given REH is due to increased tungsten opacity at the REH. This mechanism appears to be dominant in affecting the top-bottom (anode-cathode) symmetry in axial power, rather than there being any significant up-down difference in Hohlraum temperature or shock development. Additionally, we show that the insertion of two thin annular pedestals extending into the anode-cathode gap from either electrode, just radially outside of the REHs, improves the up-down power symmetry, decreases the rise time of the axial radiation, and decreases the shot-to-shot variation in the radiation pulse shape, and shock velocity. These improvements suggest that the quality of the plasma shell, which forms within the central region of the implosion, is superior to that adjacent to either electrode. Finally, enhanced emission on axis is observed, prior to the arrival of the main mass-driven shock from the impact of the wire arrays on the target. This phenomenon is consistent with the existence of a radiation-driven shock in the foam target which calculations indicate forms from radiation generated when the outer wire-array plasma impacts the inner array of the nest.