It is my opinion that the core problem of the OV, is that it proves to be illogical. One cannot hold the premise that God's nature does not change, and then conclude that God changes His mind, His choices, prophecies, or even historical events under His control, etc. That breaks the law of non-contradiction, as do most of the OV teachings. Their logic forces the only premise they can rationally hold, and that is that God is variable, unknowing, and often wrong.
Nang
We make choices all the time without changing our human nature. A personal God can think, act, feel (all presuppose change/time) without ceasing to be God. His eternal, uncreated spirit does not change to frog or tree just because He has a new thought, feeling, or action. As possible objects of knowledge move from possible to actual, God's perfect knowledge reflects this. It is possible that I will kill myself today. Since I did not, God knows that I did not. If I would have, God would have known it also. A contingent event may or may not happen. There is an element of unsettledness or we live in a deterministic matrix. Our daily choices are an illusion and God is a hoodwinker.
If God adds 15 years to Hezekiah's life in response to prayer (and He did, despite having said he was a dead duck...is God a liar or did He change His mind?), this does not change the fact that He is eternal, spirit, triune, holy, omniscient, omnipresent, omnipotent, etc.
Even classical theologians are starting to affirm weak vs strong immutability. God changes in some ways, but not in others ways. He is not a changeless, impersonal, Platonic blob, but the Living, dynamic, personal God. A being who cannot change is imperfect and less than a created being who can change as contingencies change. Change does not have to be for better or worse. It is simply an aspect of being alive, not dead.
God is triune. We say that He is 3, yet 1, and 1, yet 3. This is not a contradiction anymore than God changing His mind contradicts this not changing His essential being. God is 3 in some ways, but 1 in other ways (nature vs personal distinction). No contradiction, so ignore the JWs. Likewise, God can see history unfold contingently without having His essential nature become less than Deity or perfect.