I'd do the mods myself if I were you, I know just how I want a guitar set up, so that way you can get it exactly how you want. Pickups arent hard to replace, just a few solder points that need re-doing, so that shouldnt be a problem.
For tuning stability I'd either get a fixed bridge, or block the tremelo arm. This will also increase the sustain, of course at the expense of losing the whang bar (which let's face it, doesnt get much use unless you're hank marvin)
EMG's are good pickups, but so are dimarzio superdistortions and duncan invaders. I'd try to find out as much as possible about them before shelling out.
If you dont go for the EMG pickups, you could also fit a preamp inside the guitar to give some seriously high output which would be good for driving an amp.
Good luck!