You certainly make a lot of sense in your thinking about tone, really like the way you think!
I can agree with what has been said before. Emerald neck certainly is great, bridge too, but again, could possibly be a bit spiky.
A little more on the save side would be a Rebell Yell bridge with either matching neck or Emerald. I believe the RY neck is somewherer between the Cold Sweat and Emerald, so great for what you need. I think the bridge is a little less bright than the Emerald, but also amazing. That one just scream rock all over the place. It is tight, organic, cutting and has a nice upper mid spike giving it such a rocking voice. The general feel is modern alnico with a vitage throwback in there. Can easily do rock and punk (love it for pop punk and pop rock), 80s rock and metal, modern metal (see Red Seas Fire), etc...roll down the volume and you get blues too.
Really love the PU. Very versatile in itself and since it is very sensible to height changes it is even more so and can really be adjusted a lot.
Really all three, the Emerald, Cold Sweat (though I would pair that with a EM neck) and Rebell Yell would be amazing here and the HD, VHII and RR could work nicely too. Problem with BKPs is that they are pretty versatile so you will always have multiple PUs which can do the same thing pretty equally well, but they all do it another way, with another flavour.
Best course is probably to check out the options, get the guitar and then listen how that actual guitar you then own sounds acousticly. Then you can make an informed choice based on how bright / dark / attack heavy / etc. it actually is.