You might also try a set of half rounds. You get much of the ringing of a round wound but the smoothness of a flatwound. I have a set on my 535. I got them after I tried half rounds on my bass. No more finger squeaks, but it sounded more like an old broken in set of roundwounds than the typical dullness of flatwounds.
D'Addario makes them. $10 a set, so it's not like there's a major investment. 9-42s thru 12-52s so you have options. I tried them instead of using Elixers to quiet the finger noise.
GHS calls them "Bright Flats". Same style as D'Addario.