I may have posted this before, but I am posting this again. One of the most common pain points of having a floating bridge is doing a full string change, changing tuning, or changing strings.
This is how I do it, and since I learned this method years ago, it cut down on a lot of the pain and time of doing so (So very much less time spent tuning, adjusting bridge, retuning, adjusting bridge, retuning, adjusting bridge, so on and so forth)
1) Remove all strings. What??? This is crazy talk!!! Don't do this, replacing one string at a time makes more sense. Well, yes, if you are using same strings, same tuning, and have no other reason to remove all strings. But then again, that is not what makes a floating bridge hell to deal with. If you are not changing any of those things or need to remove all strings for some reason, just replace and re-tune one at a time. A lot easier to deal with. Otherwise, move on to step 2
2) Strings all gone, crank down the springs on the trem. Really crank them down.
3) Block the trem in the position that you want it. As in the picture, I personally just use a wooden wedge on the top side, and block the bridge on the high string side (G, B and E string) once I have the 3 low strings in, I move the wedge to the other side (keeping the bridge holding in the same position) and restring the high strings. The point is, no matter which order: Strings tight, bridge blocked in position.
3.5) Restring, stretch, retune with bridge blocked. At this point, it is all pretty easy, and much like restringing with a fixed bridge. Very simple, no one complains about that.
4) Magic happens. Remove the block.
5) Wonder what in the hell happened to the magic, the guitar is way out of tune, and the bridge is pulled really far back.
6) Loosen the screws and tension on the bridge, until it is in the position that it was blocked at.
If the strings were stretched enough, and the bridge is resting with spring tension alone as to where the bridge is blocked, the guitar should be very close to being in tune. And there you go, a nice floating bridge reset for different tuning, string gauge, or whatever was required for a full restring.
I do not do this terribly often myself, but on the occasions that I *do* need to do so, this is my approach.
Usually, I just do one string at a time, it is pretty quick and easy. I usually only do this when changing tunings (E -> Eb for example) or some other reason (As on this guitar, where I had to repair and re-glue the neck binding).
But, when I have to do a full re-string on a floating bridge, this way works well.
I would be interested in hearing any other people's approaches on this.