I've spent quite a while messing around with strats over the years and I would say the following things. Apologies if you know them all already.
Strat pickups are very sensitive to height changes, particularly the neck. Try messing with the heights, and don't be afraid to have fairly slanted pickups - you will prob end up with the bass side lower than the treble side, for the woody sound. The treble side can end up surprisingly close to the strings (with the string pressed at the last fret), but you def don't want the bass side too close - it will almost certainly have horrible overtones
2nd thing is just to make sure the actual guitar is set up properly - of all guitars strats seem particularly sensitive in this respect. For an awesome classic strat sound my experience is that you can't have a completely flat neck (you need at least a tiny bit of relief) or super low action. And also on some strats if the bridge is set up wrong (screws too tight etc) it can kill the tone.