I would see 5 as a subset of 2, which in turn, is a special case of 4. Intuition and experience are not useless per se, but they are not conclusive, either. And one is readily misled by them. I see personal experience and intuition as a way to generate hypotheses … often untestable ones, but sometimes testable, but then we are back to the scientific method in that case.
I have always liked the Dali Lama’s take on the matter: if settled science disagrees with Tibetan Buddhism, then Tibetan Buddhism must correct its thinking. So far as I know, he’s the only religious leader to accept this principle.
Technology is just applied science, so I don’t really see 6 as separate from science.
That leaves use with Philosophical and artistic exploration which, while having an element of intuition and personal experience to them (particularly WRT art), are distinct ways of looking at life and reality. Do these lead to “knowledge” in and of themselves? I think they lead to discoveries and insights which, again, where possible can and should be submitted to empirical examination, experimentation, and verification.
Art, in particular, does not really make truth claims. A cubist and a realist will have a different way of expressing, but such “schools” are generally capable of seeing themselves as personal preferences or equally valid lenses – unlike religious denominations, say. It is really a way of framing / looking at life and experience and describing one’s impressions and feelings about that.
Philosophy uses logic, reason and critical thinking to explore fundamental questions, and so is rigorous about how it functions. But to the extent it draws conclusions that aren’t testable, it is informed speculation, just like anything else.
Mathematics is also a source of knowledge. It straddles science and philosophy. It is in a sense the language of science and a tool for doing science, but meta-mathematics also gets into existential questions that aren’t fully testable.
I suppose the fundamental question here is one of epistemology. What is knowledge, and how does one legitimately come by it? To me, science is the only discipline that confines itself to what is observable and verifiable, using a rigorous and reproducible methodology. This doesn’t render other ways of observing and exploring reality without value … and in fact I’d argue that math and philosophy are also crucially important.
Science tells us how to build atom bombs, but not whether or when we should, or how we should use them if we do. That’s the purview of philosophy. Of course religions have things to say about it too, but morality and ethics are better understood without the religious cruft, which IMO adds nothing (and often subtracts much).
I regard religious faith – the basis of religion – as a failed epistemology that does not tend to lead toward an accurate understanding of reality or to a rational exploration of difficult moral or existential questions, in that it is nothing but assertions that are not only unproven, but inherently and definitionally unprovable. By contrast science is a very successful and consistently productive epistemology informed by critical thinking that does not make pronouncements about things it can’t observe.