Darryl,
What Paul is suggesting is a more common practice than many may think. Bill Callaham (
http://www.callahamguitars.com ) says the following:
"When installing a new bridge or checking the set-up of your current bridges, I recommend the following:
On vintage styled bridges the pivot screws need to be down almost to the top plate. I screw the screw down until it touches the plate and lifts the back off the body. Then back the screw off until the plate rests back down on the body. You should feel small movements, side to side and forward and back of the bridge. It pivots fully up and down. Too far down and the bridge will bind. Too far away and the bridge will slide up the screws. Both mistakes cause tuning problems.
I recommend a minimum of 4 springs for the bridges.
They should be set so that if you are doing double stop bends, the guitar remains at pitch. This means the top plate will have a slight pressure against the body. Sorry no pull ups with a vintage bridge, unless you can live with pitch problems."
I have set my Strats up like that for some time, and really have no pitch problems relating to trem movement that I know of. Eric Clapton of course has a wooden block permanently jammed in the trem cavity of his Strats to stop trem movement completely, but that is as good as a 'hardtail. IMHO, and probably not what you are looking for.
Hope that helps...........