My first thought was Irish Tours, no brainer...
Mine are in a 60s Roadworn Strat - alder body with maple/rosewood neck. For me, it does all the stuff you mention... with the possible exception of "Round, full, warm". It does plenty of that for me, but your idea of this might be different, so...
Also consider Apaches. I have them in a 50s Roadworn strat (maple neck). It's quite similar when I get into "blues-mode", slightly less woody, but definitely more "Round, full, warm". I haven't tried them in another guitar yet, but I think that they would do a stirling job on a rosewood board as well.
I put off getting Apaches for ages, but now that I have them I've found they are just a superb all-rounder strat pickup. I don't think they'd disappoint anyone who wants to get "the strat" tone out of all five positions of their strat - I seem to be able to make this guitar go in any "strat" direction I want.
I've not tried Mother's Milks, I want to, but I always end up getting something else. However, everytime someone asks for woody, all of us on here say Mother's Milks, so you have to think about those. Note, though, if I want to do Voodoo Chile type Hendrix (either the long blues track or the Slight Return single most people know), I always reach for the ITs. For other Hendrixy stuff, such as Wind Cries Mary, Apaches seem to do it better for me.
I strongly suspect that Tim has said, or will say, Apaches. Do tell us what he says, but keep it from us for a bit otherwise we'll all go "well, get them, then!" :lol:.
I am a bit of an S-S-S "purist" for my strats, so I've not really got any sensible suggestions for H-S-S. But I'd guess that Stormy Monday might be a good call.
Welcome to the forum :D