"Predestination has embedded in it choice." That can be looked at right and also can looked at wrong. That choice is part of how what is predestined comes to pass, and even that choice is itself a predestined ability, does not imply that our future choices being visible to God before he made us, was one of the ways he decided to predestine us.
But it can also be said, as the WCF puts it, that his predestining 'establishes' our ability to choose, (and, I have to say, it establishes even the choices we make).
I don't follow the structure of your sentence:
I can follow the first part, and I disagree with it. We are not equally guilty, if that is what you mean by "equally lost and incapable", but either way, the fact none of the lost are capable, and are equally dead and at enmity with God, still does not imply random choosing by God. So not only do I not follow the structure there, but I don't see how that is logical either.
If God decrees all things for his own purposes, but submits all creation to frustration, and all humanity to depravity, how is any randomness implied? He made each of us, including the reprobate, for his own particular use of each one of us.
Your last paragraph sounds like homemade philosophy. Not at all like scripture. What makes you assume we are born equally loving? Where do you come up with the notion of sin as revenge on betrayal? I don't at all follow how that has anything to do with being made in the image of God and desiring to be in the Kingdom. What you mean by "real choice" in the first sentence of the last paragraph? Are you assuming that "real choice" implies ability to choose either way? The lost, even when they suppose to "choose Christ", if it is not done as a result of God's regenerating them, are still not choosing Christ.