Yeah I think the Streamer was intended to appeal to the P/J market, but it still has that middy purr that Warwicks do, it's a lovely sound. The Corvette is basically an active Jazz bass, but again with some of that added Warwick character.
The Thumb pretty much has two bridge pickups. Mine's a '91 with the original MEC pups and stock 2-band EQ. I never solo the rear one because it's pretty thin on its own, but there are distinct and useful sounds to be had between the mix of the two and the front pup soloed.
All the bass players I know around here talk about my bass (I do have other basses but my Thumb is by far my favourite) as being an excellent instrument to play but tonally useless to them, presumably because it doesn't do that scooped Fender sound. That's a fair comment, but I love the fact that it sounds different, and certainly not un-musical, and it really pops out in a typical band mix with no effort required. And I think it makes me play more interesting stuff, because I'm not just trying to add depth to the sound like I feel I should do with a Fender bass. The same way I play more interesting stuff when I'm playing double bass, because I think the character of the instrument is interesting in itself and it deserves to be more prominent.