The Scriptures tell us that God is indeed immutable, but that He nevertheless notices and is affected by the obedience, plight or sin of His creatures. Why else, then, would Christ have wept at the tomb of Lazarus?
Then He is not immutable. Unless you are arguing that God's feelings are only external - in which case you agree with the pagan Greek concept of Immutability you just said to reject. If Gods feelings are INTERNAL, as one would expect, then God is not immutable when He grieves at the plight of sin or death.
The scriptures do not use the word "immutable", in fact that term came from the pagan Greek concept you want to divorce from and yet that is exactly how that term made it's way into the church. The word itself is absent from the Bible, so to say that "scriptures tell us" is a bit of hyperbole.
For a moral being like ourselves to change means that it is necessary to change in one of two directions- from better to worse, or from worse to better.
That's laughable and certainly not true. If I change my hair color did I change from better to worse or vice versa? If I changed my voice - same question? If I changed my mind on what watch I was going to wear - did I go from better to worse or vice versa?
That Calvinists are still putting out the pagan Aristotle's poorly thought out position that all change must be either better or worse, shows how much the idea is dying in it's own refusal to self-examine. Of course co-equal choices exist. If you chose one way and then change for another, if the choices were co-equal, then you did not get either better or worse.
To argue that a man saving a child would be any greater deed if he were white or black; would be disgusting.
It would help if the Calvinist had the courage to abandoned the failed and trumped logic of the pagans and join the Bible and it's wisdom. (Deuteronomy 14:26 - notice the coequal choices given here.)