It's interesting that you mention basswood, I normally hear that it is not very good tone-wood and needs some fairly heavy pickups to give the guitar any character.
I have a start with a floating bridge strung with .011s with a roller nut. The roller-nut gives it more sustain, but I'm going to replace it with a better one, cause it doesn't accommodate .012s, which I want to move to. Compression is something that hasn't been mentioned. You can get a lot more sustain without adding heaps of gain if you use a compression box. If I were going for more sustain I would get a compression effect pedal before I messed with my floating tremelo - I get too many nice vibrato warbles with my tremelo bar to lock it up. I don't use it to dive bomb much, just a subtle waver - and sometimes like in those surf bands where they play chords and ALWAYS add a tremelo ripple to the end.