Loren, I am not at all sure the initial singularity is really there, in a suffuciient sense to support philosophical argument. Various approaches to quantum cosmology seem to predict no singularity and some kind of bounce, perhaps a pre-big-bang existence of some sort. And Hawking famously asserted his no-boundary condition, which looks at a mere "cooordinate singulatiry (like what happens to longitude at the poles, no real geometry change there, but the coordinate system blows up. There's a topological theorem that any coordinate system on a sphere has to blow up somewhere).
But if we want to assume a big-bang cosmology for purposes of argument then I would say that within such assumption it is wrong (breaks covariance) to think about the singularity apart from the whole cosmological manifold. In other words it's the whole existence and shape of spacetime, with causality acting within it, that you have to account for and describe, not some mere pointy end of it. This I believe is what Wheeler was getting at, the observer sees it all. And I don't think it requires an embedding in higher space to do this. I know it's hard for non mathematicians to understand this, but the universe can be observed in and of itself, with its self-defining geometry, without any higher dimensional perspective. In fact this is one of the exciting things about Riemannian and pseudo-Riemannian geometry, that they do self-define themselves; from the metric you can get the connection or you can use the connection in the tangent bundle to define the metric, either way it's without any reference to stuff outside the manifold.