I can only speak for myself, but P90s and Strat pickups have in common only that they're single-coil pickups.
Very different native tones, with the P90 being bigger, warmer, rounder. Retains bite, but sounds good everywhere on the tone knob. It's also useful at all positions of the volume knob, whereas some pickups lose a lot of character when backed down. The P90 sounds good on every build platform I can think of, from solidbody to full deep hollowbody and all points and variations between - and clearly brings out the distinctive tonal response of each. The P90 may be the Universal Pickup, almost never the wrong answer.
Strat pickups, on the other hand, are beautifully tuned to the Strat and similar builds - but you don't see people putting them in other build types, because they don't translate well.
I haven't heard a Silver Sky (either series) in person, but in the demos I hear, the pickups sound similar to my description of P90s in my Reverend: open, full, sweet, singing. Not harsh and spiky.
I don't say the PRS CU22 which Mark recommended will stand in for a Strat, because I haven't heard or played one, but his "Strat on steroids" comment resonated with me, because that's exactly how I've described my Reverend. (The two guitars have different builds - the PRS, I assume, a solid body; the Reverend a thin but fully enclosed hollow body made of countertop phenolic with a partial center block and attached aluminum resonance tube. Original USA Reverends are the spiritual descendants of 60s Danelectro-built Silvertones, and worth a few minutes of online research if you're curious, but they're something of a digression here. Again, I'm just contemplating how particular pickups work in particular body builds, and marveling at the similarities and differences.)
I know if I had the wants for a Strat, it would be one of the Silver Skies. (The SE by default, because that's kinda my price bracket - and a Strat type will never be my go-to main ride/daily driver.) But every time I start to want an SS (mostly because seemingly everyone else wants one, probably), I remember that I have marvelous Strat machines in my collection already - the Reverend Slingshot among them.
Man, I keep sending myself on tangents. Let me try to refocus. Your question So, then the Silver Sky wouldn't fit the bill compared to P90s suggests that the two are alternatives to each other, and that's not really the case. A 3-P90 machine might stand in for a Strat (or a Silver Sky); a Strat or Silver Sky wouldn't stand in for any of the "iconic" P90 electrics.
Three pickups on anything will always suggest STRAT to a guitarist (though Gibson did it first with the big fat ES-5, 1949 I think). And some guitars with 3 P90s - like some guitars with 3 of any pickup - may sound somewhat, or a lot, Stratlike. But it's not because of the P90s.
The thing about P90s is that they turn every build they're installed in into a different animal, and I've yet to hear a build type that doesn't sound good with P90s. So there's no single classic/iconic P90 guitar.
In the jazz/blues idiom, there are any number of Gibson hollowbodies in the past (and some PRS Hollows) which get their distinctive character from P90s. In the pop/60s arena there's all the Beatlesque stuff with P90s in the Epiphone Casino. In classic-to-hard rock there's a whole lineage of P90s in a mahogany slab - Les Paul Special, SG... well, shewt, the Les Paul was a P90 instrument from its inception till 1958 (I think). So there's a bunch of 50s rock & roll and rockabilly.
And because P90s sound great whether clean or dirty...from country/rootsy fingerpicking to elegant jazz rhythm comps and leads to balls-to-wall crunch and scream, there's just really nothing they can't do. It's hard to have just one guitar with P90s and ever think yep, got that covered. And by far most guitars which have come P90 from the factory have 2 pickups - sometimes just 1. Rarely three. It's just that when you have 3 pickups on a solidbody...it's hard not to Strat with it.
So a PRS with 3 P90s would be a good start into the P90 domain, as I have no doubt it can cop the vibe of a 2-P90 slab rocker (think LP Special or SG), as well as a big warm Strat. And it might be all the P90 a guy would ever need, if that guy's wiling to forego more hollowbody and semi tones.
Ehh. I blather. Carry on.