OK, your playing style palette is pretty broad, makes choosing a cohesive, balanced set of pickups difficult. I'd tend to perservere with what you have. There really isn't one guitar that will do all styles, often players with a range of styles have different guitars for different styles. By replacing pickups you will also change the tone of the instrument you have and it may wreck what you already have going for it.
Realistically you'd use the bridge pickup for rock and metal & an occassional screamer solo for blues. Single coil you'd use for blues and maybe some chimy jazz tones or a bit of rock rhythm, and the neck humbucker you'd use for Jazz mellow tones and a fat lead solo sound (rock, blues, metal).
Personally, I'd go for a cleaner and lower powered set of pickups. A PAF clone in the neck, a mid powered single coil, and a slightly higher powered bridge humbucker that might resemble a hotter PAF. Use a higher gain amp, or a pedal or two, if you wanna launch into heavy metal territory. The key would be balancing the pickups so one is not dramatically hotter or quieter than the others.
I have deliberately not named any brands or models, as there are literaly dozens of them out there, and any balanced combo of these pickups would do the trick to satisfy your ears. You could also look at P90 in humbucker case for the neck, a stacked single coil humbucker for the mid and a higher powered brdige humbucker in a set up if the balance could be found. :dontknow: