I’m not so sure I’d say He is “composed of many parts”.
God is ultimately simple, and not complex.
The Trinity is that there is only One God but 3 Persons. The Father, the only begotten Son of the Father (the Word, said to be of the Father contemplating Himself, but eternally begotten, not made, and the Holy Ghost, the love of the Father and the Son.
Each Person can rightly be called God, but there is only One God.
Think of it like 1x1x1, and how that’s 1.
You’re going somewhere else with the free will thing, first of all the Church does not teach that all that matters is that you accept Jesus or Catholicism as the Truth. It does not preclude definitely that those outside of the visible Church may be saved.
But, it is also not logical to say that simply because one choice is bad and the other is great that there is no choice.
But, I find your idea theologically untenable. In truth, there is only one God. You claim that He may ‘become’ all these other gods means that God, rather than being unchangeable, is changing, many times.
It also means He presents falsehoods as truth.
It also doesn’t make sense. For instance, take Islam. It claims that Jesus never was crucified. This is in obvious contradiction with Christianity which soooorta makes a huge deal about Christ’s passion. They both cannot be true.
It also would mean that there are multiple different moralities given by God, some much more awful than others.
God most certainly can use whatever religion He pleases to do whatever He wants. But to say He is the same God as the pantheist hindus as well as the idols and clearly faulty gods of the pagans, as well as the god of the deist seems most certainly false, on an obvious level. Obviously, He at least allowed them to be created (which does NOT imply approval, just like sin being possible does not imply apporval of sin) but to say He is the same God of all of them is silly.
If He is the ever changing gods or the pagans, it does not make sense that He can also at the same time be the never changing, eternal God of Abrahamic religions.