I think we have a pretty good explanation today - it's like embeddings from AI models. Experience is both content and reference, we represent new experience in relation to old experience. That makes representation personal, being made of one's own past experience. This does not explain away pure feeling, but explains how we make discriminations of similarity and difference between our experiences, the contents of qualia, the qualitative aspects.
We also know brains are locked inside a bone box only connected to the outside world by a bundle of unlabeled nerves, there is no direct access. So the brain can only compare patterns of signals it receives from outside. But since this representation-action-learning loop is recursive it cannot be inhabited or known from outside, 3p needs to pay the price of recursion to execute in order to get to 1p.
The gap is that between description and execution, which cannot be crossed for free with cheap description. Execution costs, and that cost is part of what is like being a bat. We can't inhabit their cost pressures since we don't have their context and body. You can't remove the costs of being a bat from "what it is like being a bat" and still get your answer from the comfort of the philosophical armchair.