When I say "qualia" I mean individual instances of subjective, conscious experience full stop. These three extensions are not what I mean when I say "qualia".

Qualia are private entities which occur to us and can't be inspected via third person science.

Not convinced of this. There are known neural correlates of consciousness. That our current brain scanners lack the required resolution to make them inspectable does not prove that they are not inspectable in principle.

Qualia are ineffable; you can't explain them using a sufficiently complex English or mathematical sentence.

This seems to be a limitation of human language bandwidth/imagination, but not fundamental to what qualia are. Consider the case of the conjoined twins Krista and Tatiana, who share some brain structure and seem to be able "hear" each other's thoughts and see through each other's eyes.

Suppose we set up a thought experiment. Suppose that they grow up in a room without color, like Mary's room. Now knock out Krista and show Tatiana something red. Remove the red thing before Krista wakes up. Wouldn't Tatiana be able to communicate the experience of red to her sister? That's an effable quale!

And if they can do it, then in principle, so could you, with a future brain-computer interface.

Really, communicating at all is a transfer of experience. We're limited by common ground, sure. We both have to be speaking the same language, and have to have enough experience to be able to imagine the other's mental state.

Qualia are intrinstic; you can't construct a quale if you had the right set of particles.

Again, not convinced. Isn't your brain made of particles? I construct qualia all the time just by thinking about it. (It's called "imagination".) I don't see any reason in principle why this could not be done externally to the brain either.