im not a huge fan of the mustang myself but you should be able to achieve that low-fi stoner rock sound by just ajusting your amp setting.
and yes j has his own jazzy out now, its really nice, but! i did not like the satin neck on it, i prefer the glossy feel to necks.
you may just want to change out the pups and be done with it if you are that concerend with things.