Isn't Kahler a floating bridge? I've never restrung one, but aside from cutting off the end and clamping, a Floyd is basically like any other floating trem.
I take off all the strings (no other way to clean the fretboard and frets) but block the trem in the middle floating position before I do it. You get good at it..it isn't that hard. But it is amazing to me that a better system hasn't been invented yet. The Speedloader was a good idea but looked terrible. But it really needs to be re-designed.

I take off all the strings (no other way to clean the fretboard and frets)