It seems that the answer here is Fender.
Just in case you would consider something similar, but from another brand:
- blade, Bacchus, Tokai, and ESP are decent Japanese alternatives
- Limelight, one of the best feel J necks I've tried, nearly bought my first J
- Modulus Graphite BassStar J was an excellent fretless
- Pensa-Suhr, no wonder Victor Bailey played one
- Sadowsky is a heavy contender in good sounding lightweight basses
- you could source Warmoth or similar parts to a self-made J (with a @Kiwi neck?)
- the extra special that is bubbling under: a local luthier that is able to tweak every tiny detail to your specs