I disagree with the notion that it's faster to change strings one at a time on a guitar equipped with a floating trem. For me, it's actually faster to do all of them together. I watched my
guitar tech do something similar to this and it took him like 15 minutes (it took me like 30 minutes, but it was my first time doing it this way). I use something to hold the bridge steady (I used a plain ordinary ink pin for this purpose) and cut off the old strings. Then, string all of the new strings with the balls at the headstock, drag them over the nut, down the neck, and around the bridge. Leave yourself a reasonable amount of string to tie around the neck and cut the rest off at the bridge. Lock the strings into the bridge and then tighten all the strings up until there is actual tension on the strings. Then spend a few minutes stretching out all the strings pretty well. Then you just tune up the guitar like you would any other getting it relatively close to it's normal tuning. Give the strings another good stretching at this point and then re-tune. After that, take out whatever you used to block the trem and re-tune the guitar. After you do this a few times, you'll learn how the trem angle effects the tuning of the guitar so you can adjust your tunings beforehand. As I said, doing it this way took me about 30 minutes as opposed to the 1 and a half it took me to change the strings on it the first time (stringing one string at a time just takes too much re-tuning).