Superb post that clearly sets out the key elements that affect a material's ability to shape/respond to sound.Different properties being discussed here. Although related, hardness and stiffness are two different properties. Hardness, as in the Janka scale (or the Brinell or Rockwell scales with metal) is measured by how far a standardized shape penetrates under a standardized force. How resistant the surface of the material is to very localized deformation.
Stiffness (or Young's modulus) is the materials resistance to bending. Additional stiffness is what is gained by laminating plys together. The hardness doesn't change at all.
Typically, for a given size of stuff, the harder stuff will also be stiffer. And thus will have a higher natural resonant frequency. Also, a stiffer chamber deflects less and absorbs less low frequencies. So there are a lot of contrary aspects all playing into things at the same time.
Then you have damping. Which is the ability of a material to transform vibrational energy into heat, dissipating it. This is independent of the other two although the natural resonance points come into play as different damping of different frequencies will create different tonalities. Mixing the stiffness of materials like wood which are stiffer in some axis than others by laminating it in plys of different orientations will increase the damping. One ply will be easy to vibrate in one direction or axis but will be restrained by a ply attached to it that is stiffer in that direction. Then you have adhesive which may have a much lower modulus. The melding of different stiffness's will also damp the composite material as it won't have a predominate natural resonant frequency anymore. One of the reasons hide glues are used in making wooden instruments is that they complement the modulus of the wood, neither grossly stiffer nor softer.
That's about all this hard head can come up with late at night.
Totally hit the mark there. Of course, strength & stability are important to the sound too. The ability of the shell to withstand strains, temperature/humidity fluctuations, etc contribute significantly to the instrument's ability to remain functional. As a practical work a day drum construction, ply is almost without equal, yet still offers a good portion of the material's voice to the overall sound. That said, it cannot equal the sonic qualities of constructions that allow a more natural response to stimulation such as steambent single ply, solid, stave & segmented, but those have their downsides too. As in everything, it's a set of choices, & a decision based on "fit for purpose".And that's because a laminated wood doesn't resonate as much or as musically. There are a lot of manufacturing techniques done as a matter of course in the construction of a typical ply shell that place strength and stability far ahead of resonance and tone.