Sometimes I've found that when there are many sharps or flats, it's easier to just play ALL of them, and figure out what notes are NOT sharp or flat. But for me, it definitely seems to work well to take a tiny section of a piece at a time (if I'm having trouble with it) at a snail's pace. Then it naturally speeds up later.
A lot of gospel tunes have those 9 million flats and sharps, because some piano players teach themselves to play, and start using the black keys first (it's easier than using the white ones).