Are you stretching new strings in good???(Had to ask)
What I was told about Floyds was when tuned to perfect E standard,your bridge should sit perfectly flush to the body or flush in the pocket.
I was also told that once restrung to leave the nut unlocked set all the microtuners to a middle point so you have tuning abilitie both up and down,then stretch the strings in real good pulling then away from the fret board and bending them etc teill the guitar stays almost perfect unlocked then retune and lock it and chec it with the micro tuners.
I was also told that when removing your strings for a restring to stick a shim under the bridge to hold it in the position it was in hen tuned perfect theis will help in retuning as the tension doesnt have to keep pulling the bridge up level.
Also do you have one of those Eddie Van Halen D-tuna things on your bridge?? This changes the tension of the low EW and on a floating system subseqently changes the tension and pitch of the other strings.