Oh yes, it is very much necessary that the Senate has a say in who will shape the game in a fundamental way, call that emasculation if you will.
But the Senate is
already the most powerful elected institution in the game, and by some margin. And the Senate already has a say in the appointment of the cabinet: it even has the power (if it so chooses) to reject nominees on blatantly partisan grounds or even (and this has happened) due to personal grudges. Perhaps the administration should propose some oversight of that? Except that it would be total waste of time as it would never pass the Senate. You see the point?
Naturally.
Cabinet Minister or Cabinet Member or something similar would be fine. Although a case may exist for hiving off Forum Affairs from the cabinet and turning it officially into the civil service posting that it already is in practice.