With that budget, I'd go for the Lull with 18mm spacing and 34" scale. I haven't played one in a long time, but I was extremely impressed with every one I tried. I always thought they were the best Fender-types out there, with exactly the changes I would make to most Fenders, like flatter 12" radius fretboards and 21 frets. You will not go wrong with Lull.
But also consider Sandberg, specifically the California TT-5, and if weight matters the Superlight version. I have one, and it's about 6.5 pounds. It's a fantastic bass, though the A string has slightly low output, probably due to the flush poles on the pickup but I'm not 100% certain. (I spoke to a pickup builder who thinks the magnets under the A are probably a little weak. Could be.) The string spacing is adjustable, 18-19.5mm. Mine is set just over 18mm and it's great.
I also like the G&L JB-5 recommendation, and those are available in lightweight empress (paulownia) like the Sandberg. I used to have a JB-5, and the neck carve was wonderful. I love the 17.4mm (I think) string spacing, but I didn't like the stock 9.5" fretboard radius. (It's available with 12", but I bought mine used for a great price so I was willing to try the 9.5".) For your budget, you could go with the Custom Shop and get it seriously tricked out.