Yet CDT would have you evaluate an action by considering what happens if you replace the node Give? with a function that always returns that action. But this intervention does not affect the opponent, which reasons the same way!

This doesn't seem obvious to me. It looks to me like the graph is faulty; there should be "TheirDecision" and "YourDecision" nodes, each successors of the Give? node, such that changing the Give? node causally affects both. The Give? node is a function; the decision nodes are its outputs. With the graph structured like that, you get sane behavior.