Yeah you gotta have them finetuners at the bridge when you lock the nut. The downpressure of locking the nut throws the strings sharp.
Personally I think Floyded strats look fantastic. I've always wanted a HM strat and Tele, but never got round to owning either.

The other problem you will encounter on a traditional Fender neck is the locking nut placement. I'm not at all versed in FR Strats, but I suspect the gradient where the nut goes into the headstock is elongated. The leading edge of the nut can't change, it would throw all the frets and scale length of the guitar off. So that extra width has to go towards the tuners.
I do have a partial solution should you wish for it. A locking nut that sits behind the regular nut on the curve into the headstock. It's by no means perfect because it keeps the regular nut in play. The strength of the floyd rose is that the bit of the string that does the talking is locked down at either end. You CAN still get a bit of bind at the nut, but that's more than sortable. PM me if you want it.
You can do this, just take your time and read up plenty. Lots and lots of great information all over the internet. Ceri 12Bar and Andy will certainly advise here should you need it.

I've no patience either, especialy with paint.

At the moment, ( As I'm taking a break from plugging holes and sanding ) I'm joining a Squier neck to a standard body.
The Squier is however being redrilled for Grover locking tuners and the headstock is to be painted to match the body, as well as the resprayed with clear lacquer and the frets brought down ,dressed and polished. (it'll just take a few minutes )

_________________
"C'est parti mon Kiki "

First, I'd put my Squier up against a MIM any day. Of course, it's a MIC '97 Affinity - 1.75" (heavy) 3-piece alder body (all reg. Fender parts fit perfectly: neck, pickguard, etc., super slick neck - just great playability - since these were the first Strats made in China the parts probably came from the venerable Japanese plant that made better Strats at the time than the USA plant did. Changed pups and pots and it's a killer. I can't or won't comment on the newer Squiers, but I think the '96 (have it too), '97, and '98 were a little special. Second, if you want to change color (or add the EVH tape-look) just scuff-sand, mask, paint, clear coat then sand and polish. No need to strip. Even if you buy a used one that has dings they can be easily filled then finished. As others say, if it's the look it's one thing and if it's the tone, it's another, but even if it's both the job isn't overwhelming. Painting skills can be quickly developed by practicing on a piece of scrap pine first. Start with primer and mist coats and build up the paint slowly to avoid runs (and wear a good mask or you'll get another kind of runs, or worse). Once you've achieved a solid color just stop painting - you don't need a thick layer of paint. You don't have to sand the color coat. Then put on the clear in the same way but with many more coats because you do have to sand before polishing - orange peel has to go. The type of paint is important because different paints have different properties. Also you shouldn't mix products, e.g., lacquers and enamels (avoid enamels altogether). Some people will say nitro is the only way to go but it's not. You can use the stuff from Home Depot but you have to use the same brand of clear as you used for the paint. Rustoleum good, Krylon bad. I now use car paint exclusively - urethane that requires a 2K (or part) sealer, 2K primer, color, and 2K clear to get factory results. It's more expensive for sure but you can get any color (as long as it's been on a car or truck, or school bus) you want. I've used Surf Green ('57 Chevy just like Leo) and Cameo Cream ('68 Buick - Leo might have used it too probably but he sold the joint to CBS) on a number of builds with outstanding success. A good e-book is John Gleneicki's Paint your Own Guitar and the other is John Balmer's Stratocaster Handbook (buy it used on Half.com if you want to save $) for under the pickguard stuff, not to mention the myriad free on-line resources. Anyone can do this stuff; it's not either brain surgery or rocket science to name a few things - it's an easy step-by-step process to mod a guitar to your specs and your budget. Skills can be developed - all you have to do is be able to read, and your post(s) prove you can. Go for it.