The guy knows nuts, unless your springs are crap then u change them, not tighten them.
Look at the nut - it may need lubrication ( pencil lead will take care of this , draw inside the slot a lil and u're all set )
Tuners - what kind of tuners? You might wanna try getting locking tuners
Btw, oh floating you mean by up and down, okay I get you now.
I read up on trems years ago and their definition of floating trems is that it is not anchored onto the body for stability ( ala fender vintage ).
Maybe thats how i got confused with what you guys meant.
Anyhow, the springs should be the last place you look for tuning stability.
The main culprit is usually the tuners , then the nut.