Well I also believe in Limbo theologically however there are two schools of thought as well. Remember - Hell is not only eternal but permanent.
But as the quote I provided from the Council of Florence teaches, those who die in original sin only go straight to hell, which, as you said, is permanent.
There is Baptism of Blood and Baptism of Desire as well as by Sacrament. So the theology is not settled. And although I personally believe in Limbo - the possibility exists that Jesus himself will decide these cases on Judgement day as well. At the the Particular Judgment we are judged on how we conducted ourselves in life. So we dont know conclusively.
What determines if a person is saved or not is not what good or what evil they did in this life, but whether or not they died in the state of grace. A person could lead a completely evil life to the hour of death, repent, get baptized, and be saved. Our final fate is based, not on how we lived our life, but on the state of our soul at death. Grace, which is the supernatural life of God that is infused into the soul at baptism, is what makes us an adopted child of God and heir of heaven. If we die in the state of grace we are saved; if not we are damned. The souls who are in a state of original sin do not possess the life of grace, and therefore cannot enter heaven - even if they have no actual sins to answer for.
The Church teaches that it knows of no way for a child, during the time of the New Testament, to obtain the state of grace without baptism. An adult can obtain the state of grace without baptism, in certain circumstances, through baptism or desire or blood; but in order for this to be possible, the person must have the use of reason. Without the use of reason, a person is not capable of desiring baptism, nor offering their life for Christ. If you read the Catechism of Trent on this point, it states that adult baptism is delayed while the catechumen is instructed since they can obtain the state of grace through baptism if desire; but it then says that the baptism of children should not be delayed, because for them “there is no other remedy” to supply for baptism.
The only other way would be for a child who died without baptism to obtain the state of grace in the next life. The Church has never taught of this possibility, and in fact, if I am not mistaken, this is actually a condemned proposition (I’ll look into it and let you know what I can find).
Where does this leave us? It leaves us with exactly what the Council of Florence and the Council of Lyons taught - namely, that a person who dies in original sin only will go straight to hell.
The only two schools of thought I am aware that related to this subject is whether the souls who die in original sin suffer the pain of sense. As I mentioned in a previous post, St. Augustine and others believed they would, but the more common opinion (that of St. Thomas) is that they will enjoy a state of natural happiness.
As an aside, while reading on this subject earlier I learned that a number of theologians over the centuries have taught something that I also suspected. For a number of years I have wondered if the souls who die in original sin only will live on the earth after it is restored, as spoken of in the Apocalypse. I found out that I was not the first to suspect this. A number of theologians, including the great Suarez, believed this.