See the Theories of Well-being chapter at utilitarianism.net for a detailed philosophical overview of this topic.

The simple case against hedonism is just that it is bizarrely restrictive: many of us have non-hedonistic ultimate desires about our own lives that seem perfectly reasonable, so the burden is on the hedonist to establish that they know better than we do what is good for us, and - in particular - that our subjective feelings are the only things that could reasonably be taken to matter for our own sakes. That's an extremely (and I would say implausibly) restrictive claim.

I'm a long time committed axiological hedonist and have never believed that pleasure was objectively commensurable with suffering, and I also strongly suspect (but could be wrong) that pleasures are heterogenous and therefore not all pleasureable experiences are commensurable with each other (and the same with suffering). I find this makes it easier to explain clear cases of ambiguity in ethics, because I think ambiguity is baked into the axiological ground truth. I do believe that some things are objectively good and some things are objectively bad, but there is no universally accessible objective utility function by which you can rank all things from most to least desirable. Recognizing this clarifies weird edge cases where one form or another of utilitarianism seems to lead to a bad result, like symmetric utilitarianism leading to the repugnant conclusion or negative utilitarianism implying that we should destroy the world. These seem to be examples where maximizing hedonistic utility functions leads to bad things happening, because they are. 

Axiological hedonism follows logically from materialist metaphysics and empiricist epistemology. Good and bad are qualities of experiences rather than external events or objects, hence why reasonable people may disagree whether or not a song was good. One person's experience of listening to the song was good, while the other person's experience was bad. Projecting qualities like "good" and "bad" onto things besides experiences is to mistake the map for the territory. And if anyone doubts that pleasure is good then they just haven't experienced the pleasures I have. 

I reject axiological hedonism. I don't think anything has intrinsic value or intrinsic disvalue. On my preferred view, all value is projected subjectively onto the world, and pleasure is just one way, among multiple, to find something "good". Conscious approval is another way to find something good, for example. Things are only (dis)valuable if they are (dis)valued. I describe this view in this piece, and some more implications here.

The disvalue of suffering is self-evident from introspection, i.e. from observing how suffering feels.

Could you elaborate? FWIW, I don't really think anything is self-evident, maybe other than direct logical deductions and applications of definitions.

The disvalue is inherent in the experience; it is not a matter of an evaluation done by me, or a desire for the suffering to stop felt by me (even though there is a strong correlation), or me having a certain attitude towards suffering.

I would say suffering actually is an evaluation done by you (disliking) and a desire (wanting). The evaluations and desires inherent to suffering are kind of hardwired in, not reason-based. They are not the kind where you decide by reasoning that something is bad and to be avoided. They are forced onto you. These are empirical claims for which I think there is some evidence from cognitive neuroscience. I discuss this more in this piece and this piece.

I don't reject axiological hedonism outright, but I think it oversimplifies value by focusing only on pleasure and suffering. While both may have intrinsic value, the complexities of human experience suggest that other factors—like fulfillment, meaning, or well-being—also play significant roles. There's evidence from psychology and philosophy that suggests these aspects may be just as important in determining overall value.