This got really long. The TL;DR summary is 'there is no such thing as a little bit of postmodernism'. If qualia are anything like values, then experience is as socially constructed like consequentialist ethics, and you go down that rabbit hole.
- Has anyone given a more formal analysis of the relationship between the fact value/dichotomy and qualia?
People who talk about qualia are sure they are facts. If they are something intermediate between facts and values, much of their importance evaporates. In the latter case, since values are clearly negotiated, one can fall back on Wittgenstein to resolve the problem, by injecting the perspective that qualia are just artifacts of the social value of definitions. If red is an experientially defined parameter of our interpretation of sensory data to which we train our reactions, and not a quality, then all red things have in common is a social agreement about their likely physical effects on human beings, and not a real common content to our experiences. So to the degree qualia exist and have value, this has to remain unrelated to them.
- Does this pose a problem for higher order and self-representational theories of consciousness? Such theories try to solve the question of qualia by posting that first person experience is just a functional state(s) about other functional states.
No, injecting the social position skips over those theories to a place of greater relativism. If qualia are socially negotiated like values, then you do not need the notion of a functional state -- first person experience is a representation back to yourself of your interpretation of your experience through the social medium of storytelling. (That is why it takes time. A functional state should be achieved instantaneously, and conscious experience does not seem to be so.)
- Can one take this a step further, and argue that the fact/value dichotomy is an argument against physicalism since values do exists (even if they are not objective) and influence the way the world is?
Do bear in mind that some pain is positive, especially in cultures with things like initiation rituals and transformative models of adulthood or high values for independence and 'realism' (in the political sense, not the philosophical one -- the pain that tells me I worked hard yesterday has a positive value for 'martyred' Catholic men; the Scourge is a tool in older traditions of Wicca for invoking ecstatic states through pain; lying on a bed of nails is purifying and redemptive.)
From a point of view that takes those effects as genuine value rather than psychosocial self-manipulation, the fact/value dichotomy is an argument for social construction. At its extreme, social constructionism is an argument against physicalism: if we all have to agree on what is and what is not physical, how can that be the basis of reality? But that is far more extreme position than the idealism that simply accepts qualia as facts.