Just had a thought, and did some poking around and found some info.
If you go to
http://www.mrgearhead.com there is a wealth of info about recent fender basses (it's Fender's tech support site)
Clicking on the link for Guitar/Bass Wiring and Switching Diagrams pulls up a table of links for .pdf documents of wiring schematics, parts lists, etc. Cool Stuff!!!!
The orignal MIM Js had equal length pups and the parts list shows one part number 0036437000
The parts list for the upgraded MIM J (unequal length pups) calls out the following part numbers:
Neck 0058294000
Bridge 0058295000
The Am and Am Std J Basses have pups with the following part numbers
Neck 0033753000
Bridge 0033746000
I don't know if the part numbers are marked on the bobbins or not. If you take the pups out, BE CAREFULL. One little slip could break the hair-thin magnet wire rendering your pickup dead.
BTW, it is a typical phenomonon for a pair of full-on J pups to be hum free.
Have fun!!!!!