Qualia are not about cones in the eye.

But qualia (at least colour qualia) are often caused by what happens to cones in the eye, and the nature of your colour qualia (even ones that occur in dreams) will depend on how your visual system is wired up, which in turn will depend on the cones in your eyes.

qualia are not actual colours

Of course not. That would be a category error. Qualia are what happens in our brains (or our immaterial souls, or wherever we have experiences) in response to external stimulation, or similar things that arise in other ways (e.g., in dreams).

qualia are variables which the brain uses to denote external experiences

This seems like a dangerous metaphor, because the brain presumably uses kinda-variable-like things at different levels, some of which have no direct connection to experience.

They could be inverted

I think how plausible this is depends on what sort of variables you're thinking of, and is markedly less plausible for the sorts of variables that could actually correspond to qualia.

I mean, you can imagine (lots of oversimplification going on here, but never mind) taking some single neuron and inverting what happens at all its synapses, so that the activation of that neuron has the exact opposite meaning to what it used to be but everything else in the brain carries on just as before. That would be an inversion, of course. But it would be the exact opposite of what's supposed to happen in the "inverted spectrum" thought experiment. There, you have the same physical substrate somehow producing opposite experiences; but here we have the same experiences with part of the physical substrate inverted.

But a single neuron's internal state is not in any way a plausible candidate for what a quale could be. Qualia have to be things we are consciously aware of, and we are not consciously aware of the internal states of our neurons any more than a chess program is making plans by predicting the voltages in its DRAM cells.