Do not adjust your springs. So long as the new strings are of the same make and gauge as the previous set, the balance point should be the same.
As you have just discovered, taking off all of the strings at once is the difficult way. Even the most experienced techs avoid removing more than one string at a time unless absolutely necessary.
In recent weeks, I have been reconstructing a Charvel Model 3. It came to me with a broken JT-6 vibrato bridge. (The pot metal snapped in two along the back edge of the baseplate.) I was fortunate to source a second semi-derelict JT-6. I have since assembled the least damaged parts of two bridges into one working one. By trial and error, I have arrived at a workable float height and spring tension adjustment. Now, I remember why I prefer Kahler.