I am also a fan of Mr. Fitch ... so of course I use the "slow practice" advice, but also his other advice about "little bits fast" and "skeleton practice" where you start by playing a simplified outline and then refine the details.
Playing a whole piece from beginning to end in an insanely slow tempo is something I don't understand - really, what's the point? A character test? Challenging my patience? If a whole piece is so difficult for me that I have to play it all like an old snail, then I suppose it is beyond my present skill level anyway. If there are any weak spots, however (and there nearly always are ...

) then I find it natural to isolate those spots and work with them in detail. That is, a very slow tempo to really figure out what I'm doing.
Another little trick is to record myself - the advantage with a digital - and play it back in a much slower tempo. Very revealing! There I can clearly hear my mistakes and then work with them.
I studied classical ballet for nearly two decades. Never that we ran a whole routine through in slow motion! We worked insanely much with very, very tiny details, though, in order to learn exactly how to use our muscles in every single position. I also seriously doubt that singers ever practice their songs in slow motions, or that gymnasts do a whole floor routine in slow motion. It simply does not make sense, and it is many times just impossible as well. But I suppose everyone works with small details in slow motion. When you study a new dance or a longer combination, you "mark" the positions until you have learned the routine, but you don't waste your time and energy trying to perfect the single positions at that stage.
When I try to learn something new OR when I go back to give an old piece some "maintenance", I usually play it HS, and as slow as I need to play it without mistakes. I do not just mean "hitting the right key" but also having the right touch etcetera. Then I play it HT, often with at least one hand doing "skeletons" just to get the synchronization right. And then I refine. I always work with small parts here, because otherwise I lose both time and concentration.
When it comes to fast parts, I usually concentrate on hand positioning at first. You know, I play arpeggios as whole chords and so on. This makes it possible to play the piece in a rather fast tempo, although I don't have to move my fingers fast ...

Then I can try to work in the opposite way: slowly position my hand - play the arpeggio real fast - slowly move on to the next hand position - play that part real fast, and so on. And then try to combine two or three transitions seamlessly, of course.
I simply believe in the efficiency of working with one thing at a time. This makes the practice more fun because you can work in so many ways. (Another crazy method I have to learn the positions mechanically is to play every note with the same value and a moderate, steady tempo - works best in HS of course, and sounds awful, but it is rather effective.) I have tried to play the incremental way, by slowly increasing the tempo bit by bit - but heavens, it is insanely boring and my playing finally sounds mechanical.