I believe we share the belief that we are saved by grace by the Mercy of God.
The key word is Mercy
If an infant is viewed as not deserving hell based on their innocence , then it is not mercy that saves them . They deserve heaven based on their own righteousness, there is no mercy required...as there is no judgment that MUST precede Mercy being granted.
Your belief that all infants have their name written in the Lambs book of Life also carries the same problem
Those churches that believe in baptismal regeneration of infants , in effect believe that the infant is cleansed from sin with the water...after that salvation is theirs to lose .
That is not what the bible teaches . Salvation is an affirmative act of God . He saves us . We can not earn it , we can never deserve it, we can never lose it as it was never ours to take or lose . It is His .
The scriptures are silent on the spiritual end of infants that die, so any doctrine we have is made of mens desire not Gods word.
IF God is consistent (and we know He is) then infants like you and I are saved not because they are righteous ... but they are saved because God CHOOSES to have MERCY on them , not because they are somehow righteous in them selves . That would mean that God would be the debtor of the children ..it would not be grace and it would not be mercy
Scripture says " there is non righteous no not one." There are no exceptions listed
I could be wrong, but I believe the idea of "the age of accountability" does not state that infants are "innocent," only that God might see them as such as they do not have a full understanding of their actions. It is not (in my understanding) a doctrine which states that God owes them heaven or grace, but that God, in his mercy, grants both to them.
so any doctrine we have is made of mens desire not Gods word.
Only if we have no idea what God is like from His self-revelation, both specific and general. I do not believe this is the case. From what we know of God's nature, we can develop a doctrine. We do this all the time on things like abortion.