@chenweis suggested that a search for ductile materials could be a good goal for this project. I agree. Looking at the elastic-properties data paper, notice the K/G=5 line in Figure 2. The ratio of bulk to shear modulus, aka Pugh's ratio, "has been shown to correlate with ductility in crystalline compounds", and there are only a handful of already-computed materials in our database with "high" Pugh's ratios.
@chenweis also pointed me to a cool letter in Nature Materials from a while ago that not only discusses the potential importance of ductile intermetallic compounds, but also provides guidance towards input-space parameterization that I think could fit well with either evolutionary-algorithm or optimal-learning approaches to finding high-K/G materials.
Let me know what you think.