Now, in order to gain access to get a hex key into the saddle locking screw, we need to slacken off that particular string. I know you'll be tempted to just push the string to the side but, if you try to make the adjustment without loosening the string, the tension will pull the saddle forward and you'll be unable to control how much it moves.
With string tension slackened off, it's easy to just nudge the saddle back or forth.
After you've moved the saddle, you need to re-tighten the saddle locking screw, clamping the saddle to the baseplate again. This is necessary so that the saddle doesn't shift as you tune the string back up to pitch. To allow more adjustment range, each saddle-locking screw can be screwed into one of two holes—use the forward or rear screw-hole as needed to clamp down the saddle.
You need to do this, one string at a time, repeating the saddle movement until your intonation is where you want it.
It's tedious but that's the price of a well-setup Floyd. There is a tool called 'The Key' that can help with original Floyds. More below.
Why can't i just dump the trem?
It is possible to avoid so much detuning and retuning by depressing the trem far enough down that the strings slacken and no longer pull on the saddle when you release the saddle lock screw. Of course, you have to hold it in this position as you make your adjustments.
If you can do this easily, go for it.
Personally, I find it a bit awkward. I don’t find any benefit in doing things this way and I feel it’s less risky to go the long way around.