OP: I have had similar issues. I've tried numerous straps, basses, etc. I would suggest a remedy that combines many of the elements that others have suggested. Physio, exercise, wide straps, and of course, a lightweight bass. A physiotherapist for musicians, or a good bass teacher might be able to suggest technique-based alternatives for alleviating some of your pain. It's often difficult to find a magical cure-all, in these situations.
Danoelectrics are cheap and extremely lightweight. Probably in the 5 lb range. It would be easy to test one and see if there is any decrease in pain/soreness. That should give you a clue as to whether it's worth investing in an expensive lightweight bass or if you need to try an alternate course.
As far as your original question goes ... Scott at Birdsong Guitars now makes a Featherbass (under 6 lbs):
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I had a luthier/talkbasser (Grant Bass) build a custom shortscale bass for me. The thread is here:
http://www.talkbass.com/forum/f57/short-scale-custom-703333/index4.html
This bass came in at 6.2 lbs. I now use a 4" wide strap. The combination of the two, in addition to exercise and physiotherapy, have worked wonders--I haven't had bass-related back problems in many, many months.
Good luck!
deb