Ryle and Wittgenstein carved out knowledge-how (craft) as irreducible to the traditional propositional knowledge, Ryle gave accepting the irreducibility the scary name of anti-intellectualism. SEP even has an article about it, which also mentions in passing the third kind:"There's the kind of knowledge you have when it is truly said of you that you know a person—say, your best friend". Reducing the middle kind to direct acquaintance seems very narrow, Through a Glass Darkly poetically suggests that the scope may be broader:"Suffering, the sacred, and the sublime are concepts that often surface in humanities research in an attempt to come to terms with what is challenging, troubling or impossible to represent. These intersecting concepts are used to mediate the gap between the spoken and the unspeakable, between experience and language, between body and spirit..." In addition to episteme and techne Greeks also had a third word for knowledge, gnosis, with plain meaning of something like insight (gnostics later appropriated it for mystical revelation), as in insight into things, or knowledge-into if you will.
The technical term for suffering is qualia, and history suggests interesting dynamic for some of them. The quale of heat was reduced to Brownian motion, and we have the RGB theory of color vision, although of course "warmth" is not quite Brownian motion, nor is "color" a weighted average of RGB harmonics. Still, while an irreducible element of insight remains, propositional models can go some way. My favorite example is the modern mathematical model of continuum, we had many questions on motion, divisibility and Zeno paradoxes illustrating that it is a very crude approximation of the continuum of insight as in Aristotle or intuitionists, see Is Aristotle's resolution of Zeno's paradoxes vindicated by motion in the intuitionistic continuum? Becoming generally seems to be unaccountable for propositionally since it is not a state, or a succession of states, that obey self-identity law. As for the other SS a leading elistemologist of science once wrote three Critiques, the last two of which are dedicated to the sacred and the sublime respectively.
The issue is sometimes dissolved by declaring SSS to be outside the scope of science, but I came to doubt that such a move can work. They are aspects of reality, if they indeed furnish irreducible knowledge it has to be accounted for, if obliquely. What is its relation to the other two knowledges? What are the consequences for scientific/physicsl knowledge, usually assumed to be propositional? E.g. if SSS are irreducible "book of nature written in the language of mathematics" and "theory of everything" seem doubtful even on a materialist position. But what exactly is or is not irreducible in them (continuum seems like an instructive case study)? Is there contemporary work on non-propositional epistemology beyond knowledge-how? Most interesting aspect to me is methodological: how taking into account existence of knowledge-into helps determine what shape (propositional) scientific theories should take? How can they better compensate for the inadequacy of their medium of expression?