Floyds will not fit a standard Strat rout, but there are other trems out there which will, and which will improve your tuning stability. The Wilkinson is one, plus there are locking saddles which can retro fit onto your Strat trem.
The question is, why do you want a Floyd? If you want to do a lot of dive bombing and such, then they are the way to go. If you are just looking for better tuning stability, it will be far more helpful to block the trem so it only goes down. Then you can get the springs much tighter, and you don't have to worry about your guitar going out of tune if you break a string.
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