LaBella Fl760 are thumpy without being clanky IMO. Or some Nickel strings. I have a feeling your problem is more of an eq issue though.
They come with Nickel Strings (Fender 7250M). I like those a lot, they are far less "clacky" and bright than most steel strings, so acmeseed seems to be after a very dark tone. I find the factory strings to sound very mellow. I still use the strings that came with it end last year on my Daphne Blue '64. I never tried Fender Flats but use GHS flats on one of my Precisions. The GHS needed some time to get the sound I expect from Flatwounds, so maybe you - acmeseed - should just leave the Fender Flats on the bass, play the hell out of them and report back here in a few month it it is worth the effort?