The stock pickups are just plain noisy as they are not wax potted. They pick up interference very easily and shielding inside the guitar would make no difference.
If you try lowering your pickup height at the low E end that might help balance the sound more.
If you are looking to upgrade your Jaguar the obvious choice would be pickups. Because of the sound you want you wont go wrong with any of the Seymour Duncan 'replacement for Jaguar' pickup range. It may be worth checking their website to read the descriptions and listen to the sound samples. 😉
Other upgrades would be to personalize your Jaguar because as it is the quality is already good. For instance my sunburst Jag has a black scratchplate, and a 'fender mute' thats besides installing two new pickups (Hot rails and SD JB Jr).
May i also point out at this early stage that you dont need a Mustang bridge on your guitar. Check set up advice on this site or fenderjaguar.net.
