"There is no such thing as "a little bit saved"."
Orthodox approaches to the spiritual life revolve around the idea of theosis. There is really no English equivalent for this word. "Divinization" and "deification" are very poor translations, since they imply that we think we are becoming God.
"Sanctification" and "becoming Christ-like" really don't capture it, either, since these are ways of Protestant speaking that apply to someone who is "saved" and now is living out the implications of that. These terms to not capture the very direct participation in the life of God that we believe is possible to begin right here on earth. It is not imitation -- it is participation.
Sometimes we say that we are "being saved", in an ongoing sense, but even that doesn't really capture it, since it implies (especially when combined with the standard and honest answer of "I don't know" that any Orthodox Christian gives to the question of "are you saved?") -- a mental and emotional state of uncertainty, doubt, and fear that are just not a part of the Orthodox spiritual life. Our lives are filled with comfort, love, hope, and the knowledge of God's mercy -- as long as we actively receive it.
My analogy wasn't a great one, and you are right that analogies always break down.
The point that I was trying to make was that we want to join ourselves to Christ. We want to participate in the life of Christ. We want (in the terminology of St. Gregory Palamas) to participate in the divine energies and begin the path to theosis. We want our children to participate in the life of Christ and to be joined to the Body of Christ.
We don't baptize our children out of fear that they will go to hell or limbo (which we Orthodox don't believe in anyway) if they aren't baptized. We baptize our children for the same reason that we keep them warm, feed them, hold them, and comfort them when they cry. We baptize them because we love them -- and what more loving thing can a parent do for their baby than to join him to Christ?
Bingo! :)