I have worked on guitars for 30+ years. I have a JM, and 15 others from First Act (NOT THAT BAD) to older Epi's Harmony jazzboxes, Tele's ....more......I know, I know.
The Jag/JM bridge is a workable unit if set up correctly.
First- Put .11's on it, they way it was designed. D'Addario makes a nice set that is brighter than most (EXL115).
Then, be sure it's centered, and not rocked back or forward. Then set the height. If you have individually adjustable saddles, make sure they follow the neck contour (you'll need a few luthier tools). If you look across the strings- you'll see if they are fairly even....you may have a low saddle/string on the buzzy one.
Graphite the posts where they sit down in the body, as well as the nut. DO NOT lubricate the saddles where the strings contact them.
Everybody seems to go straight to the Mastery bridge without even trying to set these up properly, but for a savings of well over a hundred dollars, (closer to 200) it's worth it to set it up right and see how you like it.
Also- there are other aftermarket bridges that are closer to 25 dollars if you just have to change the Fender design.
Mine stays in tune and I use the bendo bar a LOT.
Thanks for listening, let me know if this works for you.