For example, two people looking at the same patch of red may have phenomenally indistinguishable visual experiences--experiences that instantiate the same property of phenomenal redness.

I don't think there's a God-given mapping from the set of Alice's possible subjective experiences to the set of Bob's possible subjective experiences. (This is why I think the inverted spectrum thing is meaningless.) We can define a mapping that maps each of Alice's qualia to the one Bob experiences in response to the same kind of sensory input, but 1) there's no guarantee it's one-to-one (colours as seen by young, non-colourblind people would be a best case scenario, but think about flavours), and 2) it would make your claim tautological and devoid of empirical content.