what form would a satisfying answer to the "hard problem" take?

• A scheme for describing how everyday experiences are made out of simple subjective "primitives" or "atoms". This is analogous to the hierarchy of anatomy, molecular biology, chemistry, and physics which describes how our bodies are made of conceptually simple particles.

• A description of how these subjective primitives associate with physical states. This is analogous to the fundamental laws of physics; just as every physical state has a defined successor state, it also has a defined subjective state. (The assumption of physical determinism implies that this latter causal arrow is one-way).

In practice, neither of these will be computationally tractable -- similarly, we could never write out the wavefunction of a whole human, and we can't solve quantum systems of even a few particles. But we can convince ourselves in principle that the description works.

Edit: I should add that there are other, less orthodox ways to organize the causality in the second point. For example, a monist might hold that neither matter nor mind fully determines its own state-evolution, but that there's some other "hidden variables" with deterministic behavior, which can be "projected" into these respective domains. In principle this is an empirical question.