Are you tightening the nut at the top of the neck? I've got Floyds on most of my guitars and don't have tuning problems with them. The knobs on the bridge are fine tuners. You should tune the guitar normally with the knobs on the headstock, tighten the nut at the top of the neck, then use those to dial in exactly. They shouldn't be all the way up or all the way down.

There are ways to make the bridge not float, but I'll leave that up to folks who know how to do it. I personally love the floating trem and hate that most of my Floyds do sit on the body, so I've never tried to do it.

Sorry if this didn't answer the question.