Here's how I got rid of my gut feeling that qualia are both real and ineffable.

First, phrasing the problem:

Even David Chalmers thinks there are some things about qualia that are effable. Some of the structural properties of experience - for example, why colour qualia can be represented in a 3-dimensional space (colour, hue, and saturation) - might be explained by structural properties of light and the brain, and might be susceptible to third-party investigation.

What he would call ineffable is the intrinsic properties of experience. With regards to colour-space, think of spectrum inversion. When we look at a firetruck, the quale I see is the one you would call "green" if you could access it, but since I learned my colour words by looking at firetrucks, I still call it "red".

If you think this is coherent, you believe in ineffable qualia: even though our colour-spaces are structurally identical, the "atoms" of experience additionally have intrinsic natures (I'll call these eg. RED and GREEN) which are non-causal and cannot be objectively discovered.

You can show that ineffable qualia (experiential intrinsic natures, independent of experiential structure) aren't real by showing that spectrum inversion (changing the intrinsic natures, keeping the structure) is incoherent.

An attempt at a solution:

Take another experiential "spectrum": pleasure vs. displeasure. Spectrum inversion is harder, I'd say impossible, to take seriously in this case. If someone seeks out P, tells everyone P is wonderful, laughs and smiles when P happens, and even herself believes (by means of mental representations or whatever) that P is pleasant, then it makes no sense to me to imagine P really "ultimately" being UNPLEASANT for her.

Anyway, if pleasure-displeasure can't be noncausally inverted, then neither can colour-qualia. The three colour-space dimensions aren't really all you need to represent colour experience. Colour experience doesn't, and can't, ever occur isolated from other cognition.

For example: seeing a lot of red puts monkeys on edge. So imagine putting a spectrum-inverted monkey in a (to us) red room, and another in a (to us) green room.

If the monkey in the green (to it, RED') room gets antsy, or the monkey in the red (to it, GREEN') room doesn't, then that means the spectrum-inversion was causal and ineffable qualia don't exist.

But if the monkey in the green room doesn't get antsy, or the monkey in the red room does, then it hasn't been a full spectrum inversion. RED' without antsiness is not the same quale as RED with antsiness. If all the other experiential spectra remain uninverted, it might even look surprisingly like GREEN. But to make the inversion successfully, you'd have to flip all the other experiential spectra that connect with colour, including antiness vs. serenity, and through that, pleasure vs. displeasure.

This isn't knockdown, but it convinced me.