This is a lot of ground to cover, and I'm really not into phenomenology, Husserlian or otherwise. But let's see.

Science is limited just like any other human enterprise is limited. It's good for certain things, not so good for other things. The scientistic mistake consists in treating every problem as a nail to be handled with the only tool available: science's hammer.

That is why the so-called social sciences are irreducible - in my opinion - to the natural sciences: they are a combination of natural science (insofar as one can carry out third-person research through experiments and observations) and humanities (insofar as one depends on individual, subjective testimony or input). Some scientists seem to have a problem with that, I don't, it's just the way it is.

What I find problematic, however, is some people in the humanities who claim that subjectivity is not just a limitation of science (it is), but also the way forward to some sort of alternative that goes "beyond" science. I think Husserlian phenomenology falls close to this position. The problem is that the whole approach seems to me to be predicated on not taking seriously one's own objections: if subjectivity and first-person experience cannot be treated by science then the answer isn't to create another "science" (or uber-science) that can handle it, but rather to accept that we as human beings are bounded to use a combination of third and first person approaches in order to arrive at understanding.

Which brings me to what I think is the point of modern philosophy: here I agree with Wilfrid Sellars, who suggested that philosophy is the discipline that can make sense simultaneously of what he called the scientific and the manifest images of the world. The first is the "image" of how tings are that we get from science; the second the "image" we get from commonsense, personal experience, and so forth. The domain of science is confined to the first; the domain of much of the humanities to the second. Philosophy is uniquely positioned to straddle the two - which is necessary to arrive at as complete an understanding of the world as we can manage.

For instance: values and prescriptive judgments (you "ought" to do this) are nowhere to be found in the vocabulary of the natural sciences. They are not part of physics, chemistry, biology, and so forth. And yet they are necessary for human living. We won't "reduce" them to science by scanning people's brains and pointing to the neural correlates of value judgments, as interesting as such research actually is. We need, instead, what Sellars called a "stereoscopic" view of things: balancing scientific and manifest images, shifting from one to the other as needed, but never giving complete priority of one over the other.