I have 2 Stingray5s and after 2 decades of only roundwounds I recently strung one of them with Magma Ultra Flats (Argentinean brand, 35€ and they're totally comparable to some 50€ LaBella LTFs I use on my fretless, justa a tiny little stiffer, but still real soft playing). Also, I've forever known and loved the Bernard thing (and many others'), knew the Ray with flats staple status (not as iconic as the P with flats thing -which I also love- but still very common). Feel so stupid for not having done this before. Flats complement the natural "in-your-face-ness" of a Stingray while reinforcing its low/lo-mid authority. I'm definitely keeping it this way, feels like the right choice for most of my fingerstyle needs (too bad I'm mostly a punk pick player, yeah, I know

).
Sorry, no low B in this song (only I've recorded with it so far), but you can get the overall thickness and articulation. Still, low B is as solid as ever on a Stingray5. But even on weaker basses I've consistently found the low B to be less of an issue when using flats than roundwounds. I've had several 5 string flat sets (both put in fretless and fretted basses) and IME they're better at "sounding like the same set of strings"/"sounding like the same bass" (timbre going to hell when playing notes on the low B string is a common complaint). I've indeed experienced roundwounds to have more variability in that aspect.