Re: What makes a really great Strat?
Sorry, complex topic = long answer...
I've only owned 4 Strats and all are/were so different in sound. I also played a fair number of Strats while looking for the ones I bought, but in my experience and opinion, Strats are like women. You can experience a bunch and still not understand them completely.
1966 post-CBS
One of the Strats I currently own happens to be a 1966 that's been modified over time, one is a 1962 reissue and one is MIM. The best sounding is the 66, but it's not even pre-CBS. The wood seems to be solid and heavy on the 66. The others are significantly lighter. The head stock on the 66 is the larger 70s type and it's also noticeably thicker; the string holes on the tuning machines just clear the wood it's so thick. The neck is laminate rosewood. When I first got it, it had a heavy BadAss-type bridge on it. It sustained like my Les Paul and I thought it was because of the bridge. The trem broke off and I put a period correct Fender bridge on and I'll be darned if it still sustained and still sounded just as thick. I've swapped out SD Antiquities and the original pickups on it and it kept the same tone; I would credit SD quality at reproducing vintage pickups on that one. The rest of the tone and sustain on the 66 seems to be coming from the body and neck, as far as I can tell. I've swapped everything else out.
American '62 Reissue
The 62 reissue is stock American-made with Fender 'vintage' pickups. It frustrates me. It has neither twang nor balls. But it does stay in tune like a mofo (I once did 3 straight 1-hour gigs without tuning, bending the hell out on solos. I don't get how it was even possible, but blew me away) and it does sound good distorted/overdriven on the treble pickup. It has a slab rosewood neck. It seems lower power and doesn't drive an amp well at all. When I switch guitars, it's the only guitar where I have to change my amp settings to preserve my overdrive/gain/playing level.
MIM
The MIM had way overwound pickups in it. Sounded ok, but like a cheap imitation of a good guitar (truth in advertising). I put Graphtech saddles thinking that would give it some sustain like my 66, but the improvement was far less than I was expecting. The neck is actually a beautiful one-piece flame maple, and it's solid and heavy (it pulls the guitar down when wearing it). I'm not sure why/how that neck ended up on a MIM, other than there is a slight flaw/knot halfway up the back of it. I was really just using it as a spare parts guitar anyway, so I threw some SD Antiquities and a Fender reissue '68 pickup in there, all lower power; kind of 7-8k type, twangy; with CTS pots. That did wonders for the MIM. I've recorded with it since and it comes across like an early sixties twanger when clean, and sounds underground/grunge/indie when distorted/crunched. I like it better than the 62 reissue, except it doesn't stay in tune nearly as well. Perhaps tuning machine changes and some different hardware might solve this.
(I also owned a Strat HM, but that was a different animal. It had little to offer for "classic" Strat tone.)
Overall, my personal experience with the 3 Strats I currently own has been:
- Electronics are the largest influence on the tone/sound
- The body wood and neck (preferably solid and heavy) provides sustain, and some additional smoothing of the tone/sound. E.g. spikes in the pickup tone seem to be tamed by the body and neck. I say this because I've swapped the wired pickguards between the 66 and MIM and listened to what changed.
- Bridges and tuners seem to trail a distant third in having any influence on the tone, sustain or sound, that I can tell.
Where would I start to build a great sounding Strat?
To answer the question, based on my experiences above, I'd find a solid heavy body, a solid heavy neck with the bigger headstock, get SD vintage/antiquity pickups, use period-spec pots (CTS) and period-spec hardware (bridge, tuners) and start there. If I wanted to bias the sound for twangy, I'd get lower power pickups in the 6-8k range. If I wanted a thicker sounding blues/rocker guitar, I'd use 7-8k for mid/neck and make sure the bridge is about a 10k, but still vintage wind using 'period correct' materials, as much as possible.
Tone caps
Something I didn't talk about is the tone cap. I've used Fender official poly caps, Sprague Orange drop, cheap ceramic disc and no-name mylar and only the Fender official and Orange drops sounded good, with a rich usable tone; like a quality wah. Newer ceramic discs and mylar didn't seem to have as deep an effect. The tone control didn't get smooth and dark, but rather just dim and muddy. When I tested those parts, I got inconsistent readings over time, so I suspect the flimsy/flat tone effect might be caused by those caps failing to release a consistent charge / maintaining their spec'd value. It's worth noting my 1966 had an old large ceramic it disc in it when I got it and sounded beautiful. Something has changed between old ceramic discs and the ones you can buy now.
(I probably articulated some of that using some incorrect terminology, but I have no doubt following posts will provide the corrections.

Sorry for the long post, but that was good to finally get out of my system.)