There's a chap on here, PhilKing, who only pops in from time to time now. His favourite strat HSS set is Stormy Monday plus Sultans (and he has a LOT of BKPs!).
Now, none of my strats is HSS, but I have both Apache and Sultan SSS sets (and Irish Tours). I also have Stormies, Mules, and Riff Raffs in various Gibsons.
Based on all this, I would try a Mule with Apaches. My reasoning is as follows: Sultans I find smoother, more polite, than Apaches. The Apaches, for me, have a rougher edge/punch to them. Considering Mules and Stormies the same way, I find the Mule is the rougher/hairier, the SM smoother/sweeter. These differences can be levelled out with the EQ on the amp and playing style - the pickups aren't a lot different to each other - but here we're talking about combining H and SS, so my first guess for getting a set that would love the same amp EQ would be to combine the smoother with the smoother, or the harder with the harder.
I'd happily give Mule and Irish Tours a go too, those would sound good together.
However, I suspect that for HSS my favourite would be the same as Phil's - SM and Sultans.
Personally, if I was into HSS, I would like to try a Stormy and Apache combination - because those two are my favourite BKPs. Especially if the strat already had Apaches and I was into them.