Whenever I change the strings (not often because it's a PITA), I clip all of them at once. I do this so I can clean the grime off the fretboard, which is something you can't do if you're changing them one by one.
So, the whole procedure takes me about 45 minutes to an hour because I usually take off the entire bridge by disconnecting the springs from the back of the guitar.
It's a pain in the ass, is there an easier way? Is there any way to stabilize the FLoyd Rose so I can change all of the strings at once and not have the bridge lean hard into the body of the guitar?
Block the bridge in its neutral position, remove the strings, clean the guitar, re-string, then remove the block.
Or install a Tremol-No™ and use that to lock the bridge before you remove the strings.