All of which are not supported in Scripture, Tradition, or Magisterium.
We naturally seek a solution because we cannot stomach the idea of an unbaptized infant suffering in hell. But all we know is this:
God desires that all be saved.
God provides sufficient grace to all human beings.
Christ made clear the absolute necessity of baptism.
The justifying effects of baptism are also attained by blood or desire, both of which require the will of the person, not his parents.
Baptism is a sacrament, which is an economy of human beings, not angels.
Because of all these, and the simple fact that God has not revealed the answer to this question, “we don’t know and entrust them to the mercy of God” is the only thing we can say.
Proferring limbo infantorum or any other opinions one way or another as absolutes is not called for, broken hearts notwithstanding. We can hope. We can entrust. But this is just one thing we cannot pronounce on. We simply do not know. One can only say, “I hope God has mercy on my child and welcomes him to heaven”, but one cannot say with absolute moral certainty, “My child is definitely in heaven.” It may be comforting to a grieving mother. It does not, make it, however, certain. The Church says, “we don’t know.” That’s also all we can say.
Oh, and for those who favour limbo, you might not really realize this, but limbo infantorum is not a third state. Limbo infrantorum is part (the limbus—rim; edge, hence, limbo) of hell. Outside of heaven and hell, there is no third final state.