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It is shown that the acoustic scaling patterns of anisotropic flow for different event shapes at a fixed collision centrality (shape-engineered events), provide robust constraints for the event-by-event fluctuations in the initial-state density distribution from ultrarelativistic heavy ion collisions. The empirical scaling parameters also provide a dual-path method for extracting the specific shear viscosity of the quark-gluon plasma (QGP) produced in these collisions. A calibration of these scaling parameters via detailed viscous hydrodynamical model calculations, gives estimates for the plasma produced in collisions of Au + Au () and Pb + Pb (). The estimates are insensitive to the initial-state geometry models considered. [ABSTRACT FROM AUTHOR]