I believe the neck has a huge influence on tone with the strat. Typically maple is bright and rosewood is warmer/woodier, but whatever wood, a good neck has a lot of vibration (you can feel it in the peghead) this is the basis to get a good sound.
My advice for a punchy strat tone is an Irish tour set because it can be used for any style, any sound (except metal I guess). On my rosewood neck 62 reissue they added incredible presence, truly spectacular! On this guitar I tried texas specials, kinman AVN 62, van zandt blues, and suhr V60LP, all good pups but the Irish tours blew them away instantly! If your guitar is already too bright, a Slowhand set could be a better match.
And if you want real hot output, you should also consider a Trilogy set, I don't know how Tim does it but they have so much output and your strat still sounds like a strat!