Well if your Grabber is that one that you can change the pickup position by "grabbing" it, hence the name

then I guess the pickup position is something like a P or a '51 P pickup position.
Not much to do regarding the pickup location on your Jazz, unless you want to re-route it, but yes, you should look for a humbucker to put in that position.
Usually Jazz-style humbuckers are stacks, which means it has a coil on top of the other, or they have a pair of coils, one for each pair of strings.
You can look for Nordstrand, Bartolini, DiMarzio, Delano, Seymour Duncan Basslines (Hot Stack), and some others...