(Perhaps using a measure of computation performed, instead of a static measure of entropy, would address that.)

This is exactly what I have been thinking for a while also. In this view, when thinking about how bad it would be to destroy something, one should think about how much computation it would take to recreate it. I think this seems like a really promising idea, because it gives a unified reason to be against both murder and destruction of the rain forests.

Still, it is probably not enough to consider only the amount of computation -- one could come up with counterexamples of programs computing really boring things...