Empirically checking efficiency and equity
Several things:


It is not clear that labor productivity as a share of GDP tracks allocative efficiency.  For example, it could rise simply because the returns to capital (capital's share of GDP) are falling, which would most obviously be a consequence of allocative inefficiency through over-investment in capital inputs.  There are potentially many other things that would confound this as an "efficiency" metric.
Gini Index isn't the only measure of inequality, and in fact it doesn't do a very good job of capturing differences in economies at the extremes of their income distributions. 
You may have the causal arrow backwards: the most widely accepted model I'm aware of (which is not without controversy, mind you) is that of the Environmental Kuznets Curve, which assumes that wage growth (not labor's share of GDP) drives environmental improvement, not the other way around. 
Because "equity" in the probability-distribution sense is attainable both by improving and destroying quality of life (e.g., everyone earns zero dollars), it's not clear that you should expect a positive correlation between this and "environmental spending".  In fact to first-order, your 50% split is consistent with what I've just pointed out.