How 'bout giving the Brice a go? To me, the words budget and 6 string sound aweful funny when put together. Haven't given it much thought. I feel anything with a B string changes the mechanical needs of the instrument a lot.
As a budget six-string user who bought a really solid, yet cheap model, all I can say is it's a lottery draw - though if you give it your usual setup the same way you did with the four-strings (plus nut and saddle fixes) you could probably bring it up to par.
On the pickup side of the game, Mike at Nordstrand Pickups, Inc. did an autopsy on the stock SX pickups and made some interesting discoveries about it. He said that the pickup had some really cool magnetic orientation/polarity features as well as interesting winding characteristics. Design paths that he would not have normally taken as an approach, but he says they have a lot of P90 design influences in a jazz shape. He also has suspicions about what's causing it to become overdriven when pushed. Mike mentioned that some time ago, Carey and the team had discussed developing a bass pickup along similar lines as a cool idea, but along with a lot of development projects, they get pushed to the back burner. At any rate, he will be sending me prototype #1 of a new jazz pickup moving in this direction for testing and feedback. Lots of variables will shift on this pickup, so I don't expect to nail it on the first go.
That should be fairly interesting. The P90 is a squat wide coil not too far from the Precision split-coil pickup, but what sets it apart from other pickups magnet-wise is the fact it uses steel polepieces surrounded by two bar magnets underneath the pickup - so the magnetic field has a different shape, very different from the standard jazz. That might be the reason for the effect, along with the mentioned fact SX pickups use ceramic magnets. I wonder what Carey'll make of it.

this is "talkbass" after all. . .