Have you seen the following dissertations: Dash (2003) Caveats for Causal Reasoning with Equilibrium Systems and Voortman (2009) Causal Discovery of Dynamic Systems?

My dissertation was initially going to be an extension of this stuff. I ended up writing something very different, but I still think about these problems off and on. If you have thoughts that you would like to share and discuss, I would be glad to chat.