As far as shortscale J basses go, I've used the SX (30") and CNZ (28.6").
I've also used a Hofner HCT Galaxie 30" scale that has an offset waist style body shaped similar to a J bass.
Not being completely satisfied with the short scale J offerings I've tried, I'm in the process of cobbling together a J style bass with a slab body I cut from a body blank of Paulownia (Empress), a favorite recycled Squier Jaguar short scale neck with Gotoh BG350 tuners, a Schaller bridge and a single hot dual coil/blade humbucking guitar pickup located in the middish position but a bit closer to the neck wired straight to the jack. So far it plays very well, sounds really good with the nylon tape wound strings I install on all my basses and it appears to be suitable for a lot of different genres including the jazzy duo I play in.