If you admit that the conscious self can exert control, you must admit to a source for that control. And if you try to define this source in terms of the deterministic activity of material elements then it is not control at all, but the inevitable reaction to previous events.
In what way can control
not be a reaction to previous events? In order to control a situation, one needs to react to the situation.
The only logical alternative to being deterministic is to be random (as was discussed at great length before) - the very opposite of control.
The function of the soul is to consciously perceive and exert conscious control in this material world.
So, to repeat my previous point (that you are studiously avoiding), how do we do that? We gather and evaluate all the information, we contemplate our options, we bring to bear our knowledge and experience, we consult our feelings, values, preferences, and beliefs. Finally, based on all that (or not, if we decide to act impulsively) we make a choice and act.
None of which is incompatible with a deterministic, material entity. So what is the soul for?