Yep, I'd go with 38th's suggestions as well, but personally I'd lean towards Irish Tours instead of Slowhands... I've found that ITs cover all those bases. I understand that Slowhands can as well, but will have more mids and give you a slightly less "woody" strat tone.
HOWEVER, all the guitars I've tried ITs in have rosewood fingerboards - I understand that some people have found them a bit bright with all-maple necks. This might depend on your amp settings I guess... but, also, I've recently discovered that MIJ/CIJ Fenders (teles/strats, both rosewood or maple board) all seem to have less top-end than other Fenders, and it seems to be in the neck, so the brightness of ITs with maple might not be a problem here?
My gut-feeling is Mother's Milks is what you want, but I've never actually tried them myself. I've thought about them and listened to clips a lot though... My first set was a toss up between Mother's Milks and ITs, I went ITs because I wanted a "bit hotter" and have never looked back that much. My next set were Sultans. I'm now considering another set for a third strat... MMs are probably gonna miss out again because I think my ITs get fairly close to the job that MMs would do for me.
On the left-hand front, I guess it will depend on whether you want staggered pole-pieces or not... If you don't, I would have thought left-right makes no difference. But if you do want staggered poles, I think BKP could probably do them left-handed if you ask (for no extra charge I'd guess?) - get in touch with them :D
And welcome to the forum :D