What you're asking for is a custom neck. Not a big problem technically, but it isn't going to be cheap. I'm not interested in the job myself, but for reference, I would charge you about $750 for it. That's complete, fretted, clear coated and ready to bolt on. That's about what most luthiers will charge. It's about 16 hours labor.
Yes, a custom neck can be made up to convert the bass to a longer scale length, without any modifications to body, bridge, or pickups. The neck ends up being a little longer than normal, like 22 frets. The pickups end up being somewhat closer to the bridge, in relation to the scale length, than they were. But, they'll still work.