Great links.
I don't think the issue is really settled. I had thought the Black and Molinaro book was pretty authoritative, but, as I mentioned, it's mostly silent on fretless instruments, other than offering photos and ad reproductions.
J W Black is a luthier who worked for Fender at the time the book was written (2001); I don't know whether he's still there. Albert Molinaro owns Guitars 'R' Us in Hollywood, CA, and collects Fender basses. The photos were taken by Dave Maddux, another Fender employee. I assumed the book had Fender's blessing, and perhaps its support as well...but Fender has notoriously ignored its own history.
Several writers have remarked on Leo's carelessness with record keeping, and Bill Carson, in his book My Life and Times with Fender Muscial Instruments (cowritten with Willie G Moseley) notes that CBS got rid of many of the historic (from our perspective) instruments left from Leo's era, to the extent that they had to go out on the open market to buy P and J basses to use as models for the "vintage reissues" beginning in 1982.
Carson also said that a number of older instruments and amps, that were deliberately preserved by Fender, were stolen by an employee and later appeared on the vintage market in the 1980s.
It's a shame that Leo never wrote his book about Fender, and equally that nothing has survived from Freddy Tavares. All we have are a few interviews, and those mostly from the perspective of guitar players, so that historically significant questions, such as, "Why a 34" scale?" never were asked.
Carson and Forrest White's books are interesting, but Carson focuses on the Tele and Strat models, and White (Fender - the Inside Story) pretty much ignores the bass and, in any case, he wasn't hired until 1954, after most of the P's history had already been accomplished.
So, we have negative evidence (the fact that none of your sources found a reference to the fretless J) against the single photo in the book.
I'm inclined, now, to think that the Js were custom order instruments. Even absent the Custom Shop, Fender always accommodated customers who wanted, for example, matching painted head stocks or block inlays on Precisions, and so on.
Thanks again for the links.