You are on the right track here, and we can use Daniel Dennett's "What RoboMary Knows" thought experiment to continue this approach. While this was developed in response to a well-known thought experiment from Frank Jackson's "Knowledge Argument", known by various names such as “Mary’s Room” or "Mary the Color Scientist", the Hard Problem claim is built on the same notions.
Here, Dennett posits a conscious, self-aware, qualia-experiencing type of robot, which knows all the relevant details of its own circuitry and programming, and also has the ability to make specific, targeted changes to its own internal state. In his reply to Jackson, Dennett tells a story in which one such robot, RoboMary, has been equipped with monochrome cameras instead of the usual color ones, but, using her* extensive knowledge of color in the environment and of color vision, she is able to calculate how color cameras would record the scene before her, deduce what changes this would cause to the state of her neural circuitry, and, using her fine-grained control of that circuitry, put it into the state it would have reached if she had color cameras. Given that her physical state is identical to the one which would have resulted from seeing in color, physicalists see no reason to suppose that this would be experienced by RoboMary any differently than actually seeing the scene in color, and would have the same consequences as doing so.
To some, this may look like begging the question, by asserting that consciousness can arise in a purely physical entity. Dennett anticipates this objection:
Hold everything. Before turning to the interesting bits, I must
consider what many will view as a pressing objection:
"Robots don’t have color experiences! Robots don’t have qualia. This
scenario isn’t remotely on the same topic as the story of Mary the
I suspect that many will want to endorse this objection, but they
really must restrain themselves, on pain of begging the question most
blatantly. Contemporary materialism–at least in my version of
it–cheerfully endorses the assertion that we are robots of a sort–made
of robots made of robots. Thinking in terms of robots is a useful
exercise, since it removes the excuse that we don’t yet know enough
about brains to say just what is going on that might be relevant,
permitting a sort of woolly romanticism about the mysterious powers of
brains to cloud our judgment. If materialism is true, it should be
possible (“in principle!”) to build a material thing–call it a robot
brain–that does what a brain does, and hence instantiates the same
theory of experience that we do. Those who rule out my scenario as
irrelevant from the outset are not arguing for the falsity of
materialism; they are assuming it, and just illustrating that
assumption in their version of the Mary story. That might be
interesting as social anthropology, but is unlikely to shed any light
on the science of consciousness.
To fit this story to the hard problem, let us first see what its proponents claim, which is that, while figuring out the physics of how the brain works is a hard problem in the ordinary sense, there is a much harder problem lurking behind it: explaining how the physics of the brain gives rise to qualia. With an intuition pumped up by the Knowledge Argument, they propose qualia are intrinsic, ineffable and private, and assume this creates an unbridgeable "explanatory gap" between physical knowledge and knowing what it is like to have experiences.
To respond, we can suppose that, instead of deducing a state corresponding to seeing something in color, RoboMary is simply told what that state is by another robot of the same type, which has functioning color vision. Just as in Dennett's original story, RoboMary, after setting her internal state accordingly, now knows what it is like to see a scene in color, without having done so. For these conscious entities, their qualia are neither intrinsically private nor ineffable, as demonstrated by their transfer from one to the other.
Of course, none of this solves the hard problem, as it depends on it being possible to make, at least in principle, a RoboMary - an artificial conscious machine - which is something not yet established. What it does show is that, contrary to what many anti-materialists believe (and perhaps hope is true), the hard problem need not be unsolvable regardless of what progress is made in neuroscience. RoboMary is plausible under the usual physicalist assumptions, which makes it equally plausible that the apparently ineffable nature of qualia is merely a consequence of our inability to examine and modify, at the neuron and synapse level of detail, the processes going on in our own brains. RoboMary has that ability, and if RoboMary is possible, so too is the communication of qualia by language.
Anti-materialists could simply assert that RoboMary is not possible, but, as Dennett says, that would not be arguing for the falsity of materialism, it would be assuming it. They might claim that RoboMary would still leave something unexplained, but to be plausible, they would have to be more specific than they have so far about what that is, and do so without tacitly begging the question by assuming qualia are not the result of physical processes (Dennett himself has made that point in various places, such as "Explaining the 'Magic' of Consciousness.")
Some anti-materialists would doubtless argue that RoboMary would be, at best, a p-zombie (something physically identical, at least neurologically and functionally, to a human, but lacking qualia.) Responding to that claim in detail (and all other claims that the definitive anti-materialist argument is to be found elsewhere than in the one we are discussing) is beyond the scope of this question; here, it is sufficient to note that not all of the many physicalism-inclined philosophers accept the argument's leap from p-zombies' conceivability to their modal possibility, despite Chalmers' closely-argued attempt to persuade them that it is not a claim that needs further justification.
One useful feature of this approach is that it avoids issues of what sort of event learning "what it's like" is. Whether it is learning a fact, or gaining an ability or phenomenal concept, the physicalist premise holds that all mental events involve, and are (in principle) causally explicable by, physical changes in the brain, and so they are communicable in the form of a sequence of physical changes to be made at specific locations (again, in principle, and only for conscious agents having the level of control of their physical state being proposed for RoboMary. Dennett's story is not, as some have mistakenly taken it to be, an argument that Mary herself would be able to do this.)
It has been said that the hard problem is only a problem for physicalists, but there is something of a double standard in so saying. Anti-materialists have been no more successful than physicalists in completing an explanation of how minds work; saying "well, it cannot be via physical processes alone" does not explain anything, and it does not mean that the question of how minds work goes away, even if it turns out that the anti-materialists are correct.
*I am following Dennett's lead in using gendered pronouns here.