I would certainly agree with the fact that Christ has both a divine and a human intellect that are wholly distinct (not that facts are predicated on my agreement ) and you are correct that my formulation can lead to a form of miaphysitism where His intellect is a composite ad mixture of the two.
I guess where I question your supposition is that because Christ could experience two distinct qualia that it leads to two distinct persons in a psychological sense. Because of the hypostatic union Christ would have “access”, for lack of a better term, to the experience of either nature/intellect. That is kinda what I was trying to get at with stretching the concept of communicatio idiomatum. While that is really more focused on the communicability of the attributes of His dual nature, I think one could argue that if quallia describes the essential self awareness of who we are that His dual qualia would exist in a unique harmony not as two separate persons, but as a union of the two.
I guess the mental challenge I have is that I do not believe that Christ’s human intellect wondered what it would be like to be divine or vice versa; he is “I AM” in both his human and divine natures. While you can describe your sense of being to me I can never experience it because we are two distinct persons, but in Christ those barriers don’t exist the same way they do for us. Everything He is can be freely shared between the dual natures at will; I strongly doubt His divine and human intellects sit there and kibitz in His head.
That is the real sticking point for me in the supposition that two intellects <=> two qualia <=> two psychological persons. I would still posit that His sense of self transcends our understanding precisely because of the hypostatic union but that his being subsists in a single person.I don’t think it is possible for him to not know Himself as both man and God.