Wow, I waited too long to get back to this thread, there's a lot of different replies to address!
First, let me share a few tricks I've picked up over the years about the vintage Strat tremolo and the best results I've been able to get. Richard, Yes, the six screws will catch after time because they wear from the pressure and friction of the bridge fulcrum points. Those are cheap and easy to replace, so when they bind, it's time to change them.
Now this is very important to the performance of the tremolo, when you set these screws for the bridge action, what you need to do is have the strings off the guitar so the base plate is hard against the body. Then, tighten the six screws down until the bottom of the screw heads are flat onto the base plate. At this point, you want to check the base plate and be sure you are not raising it off the body, that would mean one or more are too tight. Now, back off the four center screws a half turn. this should clear the screw heads from the top of the base plate. Make sure the two outer screws are still flush with the top of the base plate. This is the way to get the best performance from the Vintage Strat tremolo bridge. Now string up your guitar, and bring the tension up so you can set the angle of the bridge. I adjust the spring claw to get mine where I want them. With the vintage stamped saddles, I use the bottom of the saddle on my top "E" string as a visual reference, and when I see that part of the bridge is parallel with the top of the guitar body, with the guitar in tune, then I know I'm set.
As Richard mentioned, the nut is also a problematic area for stock Strats. The tuning machines are also another contributor to this nuisance, and depending on what type of tuning machines your guitar is equipped with, the string trees can also contribute to this. Here is how I solved this issue:
For a nut that catches the string(s), I first make sure that the string groove is clean and clear of debris. (This is assuming that you've had the nut overhauled, and the grooves are filed clean and smooth, and not factory rough cut!) I went to a music store where horns and woodwinds are sold, and bought a bottle of Selmer Cork Grease. This is not the wax stick, this is a bottle of liquid grease. When I change strings, I clean the nut grooves out with an old toothbrush, and a little of the guitar polish. A can of compressed air, will blow out anything that's still in the nut groove after I scrub it out. Re-string your guitar and bring the tuning up. After the guitar is tuned, lift each string out of the nut groove, one at a time, and add a tiny drop of this Cork Grease in the groove, and then place the string back in the groove. I use this technique on my Seafoam Green Strat, because it's the only one I still have a bone nut in it. It also has the original Vintage Kluson tuning machines on it, (I'm going to address the tuning machines next). I can dive b*mb that guitar, pull up harmonic bends, and go toe to toe with any guitar that has a Floyd on it! This little trick really stops the nut-binding!
Now, the tuning machines...here is an area that really makes a difference in the tuning stability. Locking tuners are fine, depending on the style you have in. I have locking tuners on two of my USA Strats, (1983 57' RI, and 1980 "STRAT"). The 57'RI, has Gotoh Vintage Retrofit locking tuners, which worked fine when they were new. I had these installed in 1993 when I first bought this guitar, because two of the tuners were broken at the split shaft when I saw it in the store. Now they are worn and aren't really holding the tuning as stable as they once did. I'm going to replace these with the original vintage Kluson style tuning machines. Yes, they work as well as locking tuners if you cut the string to the correct length, and install them the way they were designed. When I'm re-stringing these tuners, I pull the string through the bridge and hold it at dead stop, then I press the string over the bridge saddle, to put a bend in there where it will rest when in tune. This helps stop the slack string from slipping back into the bridge while I'm cutting the length on the other end. Pull the string past the post it's going to go into, 1-1/4" to 1-1/2" inch. (heavier strings 1-1/2", plain strings, 1-1/4"), and cut there. Insert the cut end of the string into the post all the way down until it stops. Then bend the string out the side of the post and hold it there with the tip of your finger, as you wind the string up to tension. Slip the string into the nut groove and under the string tree, (if it has one), and tune it up. Repeat this with each string. When the guitar is tuned to the desired pitch, stretch the strings. I use a Fender String Stretcher, it works great! This is the way to set up the vintage style tuners and they will work as well as locking tuners, no kidding!
The other issue is the String Trees. I replaced the original "T" style String Trees on the 57'RI with Ezyglide String Trees. These work great if you have locking tuners that have the same height string posts. They won't bind. If your locking tuners have staggered posts like Sperzel Tuners that I have on my 1980 "STRAT," then don't use String Trees at all. I don't know why, but they mess with the tuning.
I hope these tips help you guys who still struggle with the vintage stock trems on your Strats. It's really made a world of difference with me.
RG, I agree with you on the Strats with the Floyds already installed. There is no need to have a Tremsetter on those. They make them like that because this is how EVH has his guitars set up. The only advantage to that is if you break a string, the rest of your strings won't detune because of it.
EC, Not that style Tremsetter. THe ones Steve has are top mount in the Tremolo cavity, and have a hook that inserts in the spring hole on the block. Steve's guitar doesn't have the center spring, that is where one of the Tremsetters is mounted, and the other one is hooked into the same hole, but the back of the guitar body is routed with a groove, past the opening for the block, where he has the other one mounted. I don't know how he has these adjusted, so I I didn't give it too much consideration for any of my guitars.
Richard, The 3- bolt design is actually a very good idea. What screwed that up was at the time, Fender was owned by CBS who was all about the money. The more guitars they built in a month on their production schedules the sloppier the workmanship. They didn't mind sacrificing quality for numbers. 1979 was the worst year for this. It was the highest volume production year for Stratocasters, but also, it was the year that more guitars were returned to the factory from the music store dealers to have that neck pocket issue corrected. Leo Fender had a very good design there, his idea was sound. Corporate greed got in the way of it!