@freemo Not too many free lunches in nature. From this chart, the only way to get off the line common to all materials is structural - making a foam out of it. Not really an analog that can push you in the opposite direction, above the line.
@freemo If you have anyone in academia willing to help, many universities have a license to the modern incarnation of Ashby's tools, and can make custom charts with exactly the properties you want.
@freemo The relation between diffusivity (a) and specific heat (Cp) is: a = k / (rho * Cp) where k is conductivity, rho is density. So the X axis in this chart is inversely proportional to Cp, but also proportional to k (the y-axis!). The 45 degree dashed lines in the chart are isometric to volumetric specific heat.
@freemo The style of chart you're looking for is an Ashby chart. With some google-foo, the closest flavor of Ashby chart to what you want I could find publicly available is this: