I think we're just talking past each other a bit here. I agree that entropy and complexity are not the same. But I think in our case, we get away with treating them functionally as the same. If complexity lies between order and chaos and zero entropy is complete order and infinite entropy is complete chaos, the bulk of the "entropy distribution" simultaneously overlaps with "complexity".
Systems begins simple, get more complex, and eventually degrade to chaos. Analogy wise apply the 2nd Law to an ecosystem from beginning to end, if destabilization of an ecosystem leading to (or caused by) extinction isn't chaos...then I dunno what is.
Back to us functionally calling them equivalent, we get away with it, because our system (universe) is old enough that it is no longer simple, but instead complex, but not yet far enough to be complete chaos (in other words we're in the part of the 'entropy distribution' where complexity and entropy overlap).