This is just a fantastic thread and prompted me to finally jump on TalkBass, a wonderful place to discuss all things bass (and occassionally tuba, I've noticed).
What a wide array of knowledge and experiences as related to flats vs. rounds. I find myself back in the music world after a brief hiatus for a couple years and this topic really speaks to me.
I switched to flats back in 2000 and loved them. I'm a Pyramid Gold advocate, greatest strings I've ever used. I just recently ordered a custom set, gauges - .43, .60, .80, .105. I also ordered a .110 to perhaps give that a whirl instead of the .105. In the meantime I strung my '77 P-bass with an old set I still had . . . I used to hang onto all my old sets, but around the 10 year mark of playing that got crazy. I've now been playing for 25 years and luckily I hung onto the Pyramids.
I used the Pyramids on some recordings and here's a link to some samples for those that are interested in hearing what they might sound like in a 3 piece rock setting - [Invalid or Expired Link Removed]
At the time they really worked well to fill out the sound of the band and it wasn't until I read through this thread that I began to remember why I loved them so much. I had switched back to rounds years later when I moved from an Ernie Ball to a Rick, but I always felt something was missing. It's as if the flats have that true sound.
I was lucky enough to have Bass Player Mag feature the second song in the link as an MP3 of the Month way back in June of 2001, they mention the Pyramid Gold Flats . . . Man was I stoked, I'll share if I may . . .
As the OP has stated throughout this thread, the flats really create a wonderful unity regarding the band sound. They set themselves apart while blending in perfectly. For those of you not worried about dropping a little extra I really recommend the Pyramid Golds, like no other flats I've ever played.
I am once again part of the flatwound revolution.