...they only make sense in relationship to the overall system. Personally, I think limbo and purgatory were answers to theological questions which are no longer particularly relevant. (Attribute these to the writings of Augustine).

The correct theological answer should not be that these children are guaranteed heaven, nor that they are doomed to hell (or limbo). The correct answer is that neither the church nor biblical scholars can answer the question of the fate of the non-baptized - that's something that is outside of the doctrines - let the almighty be the judge over these matters.

Of course, this is not likely to be a satisfying answer to those who want a yes or no. And those on the outside of the theological systems are just happy to point out the internal inconsistencies (or loose end) - the interest has nothing to do with whether a resolution is actually possible.