I really liked CS Lewis statement that “I pray not to change God, but to change myself.” For my part, since I’m not constrained to the Catholic viewpoint by the needs of faith, able to look at this in a slightly different way. Since it is difficult to solve a problem from within the problem, I hope this might help a bit.
I see God’s immutability as having two aspects. One is the transcendent, eternal, Father, the Union with whom is the object of salvation and for which end the Son of God became incarnate. The other aspect is the immanent, temporal, Spirit, the manifestation of Whom is the Created world, into which the Son of Man, as He called Himself, was born. this immanence is immutable in its laws, while appearing to us to change due to time. It also appears mysterious and capable of miracles due to our limited and less-than-Divine perspective. Jesus the Christ embodies the Union of these two aspects of immutability as a symbol and actualization of the actual Nature of God; transcendent and immanent. This is called the hypostatic Union in your Church. I won’t go any farther with this part so as to not step on sensitive toes on here.
But as my spiritual guide once said, the purpose of metaphysical work (prayer and meditation) is penetration and the alignment of the mind with Divine Principle. What this means is that, for example, if you are going to build a bird house, you consider the purpose, means, and end of your activity. The more clearly you see these, the more refined they are, the better the final result. In a way you are “Michaelangeloing.” You are taking away everything that isn’t the birdhouse as best you see it. The participles and means to various kinds and degrees are at hand according to your ability to “see” the bird house and what is comprehensively available to achieve that.
Now, some can do that a whole lot better than others and one person may come up with a lopsided box with a raggedy appearance, and someone else might come up with the best ever grand hotel with shingles, running water, and lights for a colony of swallows. The lesser endowed builder might say “That’s a miracle of construction!” But weren’t the same tools and materials available to both? And were there different rules for each? Of course not. But as in school, maybe one was more advanced and perceptively inclusive that the other. Is the raggedy builder any less? No. That builder may be only in second grade and the other a graduate student in engineering. It is not even a real comparison. It is simply observing two points in a continuum from a point outside that thread of it.
So God is immutable both as Alpha and Omega, or the beginning of things, which means manifestation and immanence, and the end of things, or transcendence. But because modernity from Augustine to Copernicus, give or take, focused on the transcendent and now we have science and its monological view focused on immanence, we seem to have a conflict where each perspective claims ownership of the whole dynamic. Neither does. The conflict is a matter of partiality and framing. Each “side” is expert in its field, but looses by not including the other. A dysfunctional marriage on the verge of either divorce or reconciliation, if you will.
It’s your call. Fro my part, I like this statement: “When you call yourself an Indian or a Muslim or a Christian or a European, or anything else, you are being violent. Do you see why it is violent? It is because you are separating yourself from the rest of mankind. When you separate yourself by belief, by nationality, by tradition, it breeds violence. So a man who is seeking to understand violence does not belong to any country, to any religion, to any political party or partial system; he is concerned with the total understanding of mankind.”~ J. Krishnamurthi
Now I’m not saying that you shouldn’t be a Catholic or a Jew or a Muslim, but we all need to be aware of how things work in God’s picture as distinct from our best and most sincere stab at what it’s all about. Just as it has been said that “Civilization is a battle against testosterone,” so might actual Catholicism in its original sense be a battle against mental limitations on God. Or for Grace.