On second thought, this is Pyrrhonism, not Academic skepticism. It does point towards a simple 'suspension of all beliefs' rather than any true declaration of doubt.
Although this commonsense approach is intended to use as few suppositions as possible, it does make
some. Even though we can only declare a sensation to be 'directly experienced' through the use of some kind of assertion (which seem inherently fallible), qualia seems to be quite a different thing than belief. So I might be presupposing, incorrectly, that qualia is in some way subject to 'mistakeness'. I don't know; either view looks hard to parse.
The only approach I've uncovered that seems to have a chance at actually refuting this might be Duncan Pritchard's claim that underdetermination - which is essentially my core supposition - is false, or somehow inapplicable (in his words: a contentious philosophical claim masquerading as common sense). So I guess I have one promising avenue to explore, at least, even if underdetermination feels basically true to me.
Thanks to everybody who responded.
If you know something there's no need to "know that you know," anymore than if you're running, say, you need to "run that you run." "Knowing that you know," among other things, seems to suggest that there is, or needs to be, something certain about knowledge, and as I've expressed a few times, that is a mistake.
A big problem with philosophy is that it very easily becomes a meaningless semantic game. When I talk about 'knowing that one knows', I'm not asserting that it is possible to know something yet not know that I know it. Rather, the statement is used to highlight the infinite regress of justification which fallibilism creates (how do you know A, and how do you know your explanation for why A is true, etc). The incoherence is the point.