I don't think it would be so much as a switch of dimensions but an object that is sort of forbidden by a few laws of physics. So the true internal structure of a black hole will probably remain speculative. My comment about it not having to be a singularity is mostly to address the issues with the model. Iv heard a few people basically say that because a singularity is a physically impossible object, it means that blackholes cannot and do not exist. So to suggest that basically there are theoretical ways in which you may have exotic matter or could imagine a similar principle of having degenerate matter basically hold up the structure.
Example of confusing properties
Conservation of angular momentum.
A singularity - that is a object that has zero dimension, cannot have the property of rotation.
Entropy
Entropy is the measure of disorder in a system, and disorder should always increase in a closed system. The singularity has zero volume, so, it should have infinite order (?i think thats the right way around)
How there are ways in which those issues have been modelled from a thermodynamics standpoint, basically in a manner of speaking, associating properties to the event horizon, despite it being a virtual surface. Also it is clear that a blackhole can have the property of rotation in a known spacial axis, based upon what we know about quazars and accretion disk formation, which if the blackhole didn't rotate or have any associated property, the disk would not form, material would simply fall onto the event horizon...
anyway... lol this is getting a bit involved

and I rapidly approach the limit of both my comprehension of the theory and my memory of it too lol