If Strange Magic has left the thread I'm more than willing to take up for the "subjectivist" side.
The more I've had this discussion (not just on here, but elsewhere), the more I've come to realize that the terms themselves are at least partially to blame for why and how people talk past each other. At the least I think I've found four slightly different definitions people seem to be using when mentioning objectivity/subjectivity:
Subjectivity = Mind-dependent things or "individual opinion"
Objectivity = Mind-independent things or "facts not amenable to individual opinion."
There are probably more subtle definitions than this, especially with objective where I've also noticed a definition close to something like "unbiased."
To me, it's quite obvious that any notions of greatness, good, better, best, etc. do not exist as properties of objects without perceiving, feeling, thinking minds that create values and standards based on what they like/dislike. These values and standards can point to objective features of music, but this is very different from saying the greatness is IN those features that we like. This also doesn't mean all artistic judgments exist only as individual opinions. We do, indeed, have have the standards and values formed by groups whether they be as small as a sub-sub-sub culture devoted to a rather obscure genre of music, or the standards of a society/culture over long periods of time. The latter are valuable in large part because they determine what music survives for future generations to discover. It's fine, of course, if you only decide to care about what music you like/enjoy, but to me part of the reason to engage in discussions about greatness, canons, etc. is to play a role (even if it's a minor one) in determining what music is heard in the future. In a way it's a kind of Darwinian approach to aesthetics.
I think the difficulty of this subject is bound up in the messy tangle that happens in the interaction of subjects with art objects. We experience an art object and our reactions (aesthetically, emotionally, intellectually, etc.) themselves are an incredibly complex web of cognitive phenomena influenced by a billion different things that we can have vastly different levels of awareness of, ranging from our socio-cultural conditioning to our individual personalities and tastes to our knowledge about the art in question even to all of the evolutionary psychology that underlies why we appreciate and value art in the first place.
As far as I know, nobody has come close to unraveling this entire mess, though I don't doubt there are steps being made towards it in science that, at the very least, can alert us to some of the unconscious cognitive factors that go into shaping our aesthetic opinions and values, both as individuals and in a larger socio-cultural context. EG, I find it fascinating that generally people's music tastes tend to peak around their teenage years, with the music they latch onto during that period usually remaining lifetime favorites; and declining as they get older, resulting in the cliched attitude of "music in my day was so much better than the crap that's popular today!" Obviously such a phenomenon doesn't describe everyone, but clearly it's a common thing and must have some psychological/neurological underpinning. It's just one example of how I think science can move towards helping us understand why react to art how we do.
I also think the objectivists have a point in that certain things--like the continuing appeal of the "great composers" like Mozart, Bach, Beethoven, and their "masterpieces" over time--scream out for an explanation of why/how that happens. It's a truism that such composers/work are considered great people people continue to think they're great, but explaining why they think/continue to think that is another matter entirely. It could very well be that such great composers/works managed to tap into something that appeals to very fundamental elements in our psychology, allowing them to be appreciated/enjoyed across times/cultures and even by people who aren't well-versed in the social-cultural particularities of the era in which they made their music; but even if that's the case I would still caution against claiming this is any kind of "objective" standard for greatness. What it is is an explanation for why so many subjects think such things are great. You may think that's splitting hairs, but we're still also left with the problem that there is zero music that appeals to everyone, and even the enduring composers/works have relatively little stake in the big picture of all the music out there that people now like.
I would also like to applaud OP for suggesting that we move towards something like a reductionist approach to this issue in which we do try to consider these subjects more piecemeal rather than the big generalities that tend to get spoken about. As much as I'm interested in the subjective/objective distinction from a philosophical angle I do think it would be more useful if we took to discussing the "complex interaction between subjects and art-objects," but part of that has to come with a recognition that the subject, at the very least, plays an equal role in that interaction; that standards/values aren't God-given, aren't found in nature the way rocks and trees are, but are created by human minds with biases and values relative to their time, their cultures, their biases, personalities, individualities, etc. There's something that can easily happen in human cognition when standards are shared by a lot of people within a group that people start thinking those standards have an existence as objectively real as the sun and ignore the fact that they were originally created by other human minds that had their own biases and values relative to the things listed above. It's GOOD to question such things, even if we end up accepting them as our own.