I can hardly see them you are correct.
To me the most likely thing I can think of that "moves around fast" and is hard to kill are fungus gnat larva.
I use mosquito bits/dunks in the water for the plant and have even shaken some mosquito bits into the media.
That will kill fungus gnat larva.
The sprays and soaps only kill the adult flies.
Pyrethium kills most everything else at least to the extent of seriously decreasing the population (aphids, mites, mealies, scale etc)....so that is why I am thinking the fungus gnat larva if truly your methods have not put a dent in the infestation.
Furthermore, fungus gnats are a sign your plant needs to be repotted as they are attracted to rotting media. So even if your plant is healthy, I'd do a repot before that changes