Evidence for high-Tc cuprate superconductivity is found in a region of the phase diagram where non-superconducting Fermi liquid metals are expected. Cu valences estimated independently from both XANES measurements and bond valence sum calculations are greater than 2.25 and are in close agreement with each other for structures of the homologous series given in the title with s = 1, 2, 3, 4 and 5. Two questions arise from the present perspective: 1) Is all the action in the CuO2 layers? 2) Is there superconductivity beyond the usual dome? The record short apical oxygen distance found in the homologous series especially in the s = 1 member, at odds with the current theory, suggests the possibility of a new pairing mechanism. The apical Cu-O distance in the s = 1 member decreases upon oxygenation from 2.29 to 2.15 dot A while the Cu valence increases to 2.45 dot A.