The reason for this is because the JB has changed spec from the original version you hear on those recordings from 20+ years ago.
5150, Ash is a really really bright body wood! In my hard ash Strat, I have a lowish-output HB in the bridge (A VHII) which only has about 9.5k DC, and it still has a lot of brightness. I'm having a switch put in it now that will have 2 levels of resistance available to tame the high freqs.
As for SD pickups, I think a Screamin' Demon is a much better choice for the Strat than the JB. Just use a bit more gain, if needed.