This company could make some tiles that are 12" x 12" or 12" x 24" http://slate-ish.com/tile/ We are not looking for an attractive color as these squares can be glued to the inside of the speaker. We could also add some grooved channels in the MDF/Baltic Birch to add Green Glue. Perhaps the front baffle or large portion could be cut by Slate-ish? The source of the material for this company is sink cutouts from kitchen installs. Think about that size for ideas.
I know Wilson and Vapor Audio uses these types of materials in some of their designs.
In their FAQ they have the following
"Can I order custom shapes or colors?
Sure you can! We like a challenge! There will be a set-up fee and the end price may have a minimum order quantity. Please contact us with your idea and we will develop a quote for you."
All in all perhaps there is no silver bullet but combining materials like Baltic Birch Void Free Plywood, Green Glue Channels, and Phenolic large tiles gets a good mixture of materials with different resonance properties and densities.
One thing is for sure, as we move up the chain with better drivers and wave guides the Speaker Box becomes more important!!