If you look at the basses that Family Man and Robbie use, there's nothing special going on pickup wise. And they used a lot of different basses, from Fenders to Steinbergers. In all likelihood just the stock pickups.
First thing is to use flats and turn your bass' tone control down!
You shouldn't expect a pickup to get that tone, you have to get that with the amp's tone controls, just like they did.
Agreed, except neither roll the tone off much at all. Much better to get a nice full range tone from the PUPs and bass while getting your fatness from your fingers or thumb, and EQing your amplification to roll off the highs, cut high mids, and boost low mids, for example.
Aggressive PUPs won't sound great at the massive SPLs reggae bassists typically strive for; instead look for roundness and balance, IMO.
I've heard tons of differently mixed versions of the same master recording of various riddims, and when the bass is mixed cleanly rather than with a lot of bass boost you can hear how evenly the bass is recorded. There are many approaches, but most often the huge clean tones associated with various reggae bassists are based on post bass EQ or from that and a combination of EQ at an onboard preamp. Rolling off the tone on a passive bass leaves a lot less signal to play with, but YMMV, of course.
Also, live a lot of the warmth often comes from the 18" PA subs, too, for example.
I really don't agree that a Gibson mudbucker tone is or has ever been a major part of dub tone from any era, though I've seen them used very occasionally.
