We write your utility as a function of your actions and the mailer's actions based on ambient control. This allows us to consider what would happen if you changed one action and left everything else constant.

It doesn't (at least not by varying one argument of that function), because of explicit dependence bias (this time I'm certain of it). Your action can acausally control the other agent's action, so if you only resolve uncertainty about the parameter of utility function that corresponds to your action, you are being logically rude by not taking into account possible inferences about the other agent's actions (the same way as CDT is logically rude in only considering the inferences that align with definition of physical causality). Form this, "sacrificial action" is not well-defined.