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.
Update from Fender. The SL5X was a fender special run that featured an HSH pickup configuration and blue burst finish. Other than that it's the same as a series x soloist.
Ordered a Jackson Soloist which will be here today. Ordering a Positive Grid Spark 40 in the next couple of days. I imagine I'll use downloaded presets for the Spark 40 that resemble popular thrash metal setups since that's mostly what I play. But I will also browse other presets.
I just jam in my bedroom for funsies. No plans to play shows or anything.