Is your strat an Alder or Ash bodied? Ash tends to be a lot brighter than Alder so i'd find that out first. Also remember that different Amplifiers have their own unique characteristics, so what amp do you have? I might be able to help you out. Given i've never played a BK pickup in my life (thats about to change soon) but I do know a lot about Amp EQ's and different woods used on guitars and so on and so forth (not to sound c--ky).
FYI also, i've got an Ash bodied strat with an all Maple neck/fretboard. It's a very bright guitar and I installed a Dimarzio Tone Zone into it a few weeks ago. I can't tell you how pleased I am with how well it worked with my amp. Some people wouldn't really think so just by telling them what kind of guitar it is, but my amp has a very Dark and scooped characteristic to it, so I use brighter tone'd woods to balance it out. You just have to know what you need more of as far as your EQ and guitar woods.
One thing that helped me out a lot is playing through different amps, I sat down one day with a Marshall DSL combo and didn't like it cause no matter what I adjusted the EQ too. It was too brittle for my taste, that was when I realized that Amps themselves have their own unique personality just like guitars do. Not saying that one Marshall amp is gonna sound the same as another but it helps you close in on what you're looking for.
Cheers.