Many people take it as a given that positive experiences have intrinsic value, but I don't think the matter is as clear-cut. So here I present a simple experiment which you can try if you are in the mood for listening to music.
Experiment: Listen to some music you like. After a while, mute the music. Alternate between silence and music while trying to appreciate how each feels.
When I mute the music, there is a lingering freedom from what I like to call the "heaviness of being"—basically any pain, unease or listlessness that I may otherwise feel. Turning the music back on definitely adds an enjoyable or gripping quality to the experience. But when I mute it, I don't really get the sense that the experience has become worse, and yet I don't find the peaceful silence better than neutral. This would seem to imply that listening to music is at best neutral.
To be clear, experiences can be impactful and leave a memory associated with meaning and value. Some event can cause me to feel deep sadness and still have this effect, even though I would hardly consider the moment-to-moment experience positive. And my aim here was precisely to call into question the intrinsic value of pleasure, its value when experienced for its own sake. I am curious about your thoughts if you tried the experiment!
When I said earlier that some people form non-hedonistic life goals, I didn't mean that they commit to the claim that there are things that everyone else should value. I meant that there are non-hedonistic things that the person in question values personally/subjectively.
You might say that subjective (dis)value is trumped by objective (dis)value -- then we'd get into the discussion of whether objective (dis)value is a meaningful concept. I argue against that in my above-linked post on hedonist axiology. Here's a shorter attempt at making some of the key points from that post:
Earlier, when I agreed with you that we can, in a sense, view "suffering is bad" as moral fact, I would still maintain that this way of speaking makes sense only as a shorthand pointing towards the universality and uncontroversialness of "suffering is bad," rather than it pointing to some kind objectivity-that-through-its-nature-trumps-everything-else that suffering is supposed to have (again, I don't believe in that sort of objectivity). By definition, when there's suffering, there's a felt sense (by the sufferer) of wanting the experience to end or change, so there's dissatisfaction and a will towards change. The definition of suffering means it's a motivational force. But whether it is the only impetus/motivational force that matters to someone, or whether there are other pulls and pushes that they deem equally worthy (or even more worthy, in many cases), depends on the person. So, that's where your question about the non-hedonistic life goals comes in.
People choosing life goals is a personal thing, more existentialism than morality. I wouldn't even use the word "value" here. People adopt life goals that motivate them to get up in the morning and go beyond the path of least resistance (avoiding short-term suffering). If I had tto sum it up in one word, I'd say it's about meaning rather than value. See my post on life goals, which also discusses my theory of why/how people adopt them.
If you feel that we're talking past each other, it's likely because we're thinking in different conceptual frameworks.
Let's take a step back. I see morality as having two separate parts:
Separately, there are non-moral life goals (and it's possible for people to have no life goals, if there's nothing that makes them go beyond the path of least resistance). Personally, I have a non-moral life goal (being a good husband to my wife) and a moral one (reducing suffering subject to low-effort cooperation with other people's life goals).
That's pretty much it. As I say in my post on life goals, I subscribe to the Wittgensteinian view of philosophy (summarized in the Stanford Encyclopedia of Philosophy):
Per this perspective, I see the aim of moral philosophy as to accurately and usefully describe our option space – the different questions worth asking and how we can reason about them.
I feel like my framework lays out the option space and lets us reason about (the different parts of) morality in a satisfying way, so that we don't also need the elusive concept of "objective value". I wouldn't understand how that concept works and I don't see where it would fit in. On the contrary, I think thinking in terms of that concept loses us clarity.
Some people might claim that they can't imagine doing without it or would consider everything meaningless if they had to do without it (see "Why realists and anti-realists disagree"). I argued against that here, here and here. (In those posts, I directly discuss the concept of "irreducible normativity" instead of "objective value," but those are very closely linked, such that objections against one also apply against the other, mostly.)