I'm not sure I understand you. What do you mean by the system of equations being undetermined. Are you saying to take the same animated gif and not alter the actual physics in any way, and just refer to it differently? That obviously doesn't change anything. You need to alter the causal structure.

My problem with non-machine functionalism is that any reason we have to say we're conscious would equally apply to a simulation. If you one day found out that you were really a simulation would you decide your consciousness is an illusion, or figure you must have gotten it backwards which one is conscious, and it's the simulations that are conscious and the real people that are p-zombies?