Maybe put your bridge a bit higher. I call pull up to 6 half notes up now that I put my strin/bridge high at 3,5mm (24fret). And the good thing is that the notes fret out exactly when my tremolo is hitting the bottom of my guitar. So that's perfect!
I used to play at around 1,8mm (24fret) but with a higher action I can mute notes better and put some more emotion in my playing. The only thing that I don't like about a high action is that I miss some "chucca chucca sound" when playing rythm work. But everything has it's disadvantages I think.
So first try to increase you action. I shouldn't slow you down that much raising it but it will sound better.
