The burden is not on me to show that science produces a model that may or may not correspond to some actual that forever lies inaccessible. Speaking of science as if it were in a model/absolute framework, however, follows the same pattern of the picture metaphor in which we draw an analogy for what we say or claim to a picture or painting of an object. The metaphor is fine, but in philosophical discussions I think you can resolve some issues by noting the figurative aspects of the language. We don't have to seriously worry if our theories are literally asymptotically approaching some absolute or not if that is just a figure of speech.

As for the question “Is the scientific method obsolete (because modern research methods don't produce models or underlying mechanisms)?” my answer is: No, it is not obsolete. The scientific method doesn't produce models, strictly speaking, nor does it always reveal an underlying mechanism. Both Newtonian and quantum mechanics succeed quite well without specifying an underlying mechanism.

Philosophies often run parallel to each other. They say some of the same things in different ways. If you are trying to pin me down to a well-known philosophy, it's probably somewhat like later Wittgenstein (Philosophical Investigations) or Gilbert Ryle (Concept of Mind), but really, all the blame lies with me.

In noting metaphorical aspects of what this or that person says, I am not criticizing; I am trying to clarify by offering another way of looking at the matter.

We are not shielded behind models or representations from a reality which is “underlying” or otherwise always just out of reach. Our actions have consequences, so it's not “anything goes.” We are up to our necks in an enveloping reality and must swim to stay afloat. Science, and all branches of learning, teach us how to swim. Swimming, to use a different metaphor than the picture metaphor, is not a model or picture of anything else. You either do it well enough or you don't.

That's all I am saying. Once you acknowledge the figurative aspects of language, and recognize when they have creeped into a philosophical discussion, you can momentarily set such notions aside and look at what people actually do to succeed, to fail, to recovery from failure, to improve, etc.

Look at what is going on here. You act to resolve a problem in the world that you are temporarily engaged in. You ask a serious of questions to prompt suitable feedback from me. There is no model that you amend. Rather, you refine the way you will deal with me, interpret what I say, disagree with me, and so on. The way we interact with each other is changing by the give-and-take of this discussion.