This weekend I went to Vienna where I found a shop (Klangfarbe) which had some Fender Jazz American models on display.
From Deluxe series they had only a 5-string, and they also had couple of 4- and 5-string Standards.
I have checked the string positions at the bridges, and they were different on each bass, so I guess they have replaced the strings at the shop and did not put them back as they were originally. But I have found one 4-string Standard with the 19 mm setting which I assume is original (each saddle has the string in the groove closest to the middle of the bridge).
I have tested the Deluxe 5-string (white, alder body, rosewood fingerboard).
The string action was excellent (low), the neck was close to perfect I would say.
But I was expecting better pots (they are plastic and do not feel very solid when turned), and I also strongly believe that the Deluxe model deserves nicer pickguards.
Also, the N3 "noiseless" pickups were not noiseless when the pickup balance was uneven.
I also found myself to prefer the passive tone to active one for some reason, but as I have always played passive, this might be my specific problem.
And I still do not know what to do with the 5th string. Shame on me.
So I tried the 4-string Standard (black one, no idea what wood is the body made of, with maple fingerboard). I liked the sound somewhat less than the passive sound on the Deluxe 5, and I was disappointed by the look of the maple fingerboard (there is no optical separation between the neck and the fingerboard, it is one piece of wood, so it does not look very attractive), and also the edges were sharper than on the Deluxe.
So, now my choices are narrowed down to either 4-string Deluxe, or 4-string Marcus Miller, which I have yet to test somewhere, but I hope I will like the maple fingerboard on MM more than that on the Standard as it should have white binding.
Over the weekend I have also made a test on my current bass, which has a bridge with adjustable sting spacing. Normally I have set it to 20 mm, but now I have set it to minimum, which is about 17,5 mm !!!, and I was really surprised that I can still slap and pop it very comfortably, and also play with my fingers very fast. I have also enjoyed the extra space on the sides of the fretboard.
So at the end of the day I figured out, that it is not the tighter string spacing of the 5-string basses which makes them difficult to slap for me. It most probably is the 5th string which stands in the way.