I have an X series Jackson Soloist. Absolutely change the screws. Also next time you have your Floyd Rose out, tighten the whammy bar post on the bridge itself.
As for tuning. I usually tune G, D, B, A, HIGH E, LOW E. If you have the bridge blocked off (I use a broken pencil with masking tape wrapped around it until it's the right thickness), it really does make it easier to tune that way. And always tune in the playing position as gravity will affect the tension of the bridge.