Late winter I got on the tapewound bandwagon too. Tried D'addario, GHS, Roto Trubass black nylons. The D'addario D string broke from switching it too much between basses. GHS was OK, but I was looking for more of an acoustic sound. The Rotos were too stiff. Then I think I read beate_r recommend the Pyramids:
I tried them and really liked them. I tried them on my Fender PJ, my Tacoma Thunderchief, and my Wishbass JB. Currently they reside on the Wishbass (with a Haeussel mag and Pickuptheworld Piezo pickup). But I'm going to get another set for my Tacoma. The Thunderchief has a set of TI flats on it now, for a modern acoustic sound. But I have a Takamine TB10 due tomorrow, so I'll use that with flats and go back to Pyramids for the Tacoma, which I think is a more optimal combination. I love the papery, velvety feel of the Pyramids--totally different from the other black nylon strings I've tried. It's strange they haven't been mentioned more on this thread. If you're after an acoustic sound, they are definitely a variation worth exploring. They worked well on my PJ too, with emg pickups, but right now I have a set of Labella whites on it, and I'm digging that sound as well (in my case it also took a while for the whites to be delivered).
On my other basses I have Thomastik flats--they're kind of my default strings--but I recently experimented with Kalium nickel roundwounds and those things are great on a fretless for getting a quasi fretted sound. On my six-string Fender Jazz I'm thinking of subbing the TI flats with Labella Black Nylons just to see what that would sound like. So I might be down to just two basses with TI flats, a Warmoth fretless five-string and a Warmoth Jazz, both still in production.
Anyway, thanks everyone for turning me onto nylon strings! It's been fun exploring yet another bass parameter. I think it will take another 6-12 months before I settle on nice string/bass pairings for all of my harem.