That's incorrect, sinkspur. You can put them in Hell, beccause Hell is not *necessarily* a place of punishment and natural suffering.
But, limbo says they can't go to heaven either, substituting an absurd notion of a place of "natural happiness" for souls that were made for God.
Why is it absurd? Even the pagans believed as much.
Hell has been a place of punishment since the Crucifixion freed Moses, the prophets and the faithful Jews.
That pagans believe in limbo does not help your argument. Augustine, in a moment of lucidity, said "Our souls are made for God, and they are restless until they rest in Him."
Our souls are made for God, and He wants them. It seems odd that He would place souls that had never committed any actual sins into some happy penalty box.
Since nobody knows, you are free to believe whatever you want. I would caution, however, attempting to explain your theory to a woman who has just lost a child who was not baptized.
It won't be comforting.