I have a strat with a Foyd Rose on it, but it's not with the floating bridge. I mostly use it on blues gigs every once in a while, and that's the only guitar I have a whammy on. I don't use it a lot, but I do have a way to keep it in tune.

Stretching the strings is important, but so is this next step. You have to warm up the neck, before you tune it. Just play some licks with or without volume for a few minutes, and make sure you cover as much of the fretboard as you can. This will warm up your neck, and then you tune it up.

When you stop playing and put the guitar down, the neck will cool down and this usually makes the strings a little sharp, but when you pick it back up and start playing again, as the neck warms up you're back in tune. I just check my tuning at the end of the set, and stay in tune all night. I know some players that jump on stage and tune up, and then when the neck warms up they're out of tune. Then they make an excuse about the guitar, or tell the old joke about it being in tune when they got it while they tune up again. I figured this out after being on the road for few months, and I've been doing this for 15 years now. This really works on any guitar with or without a whammy, but if you're really heavy on the whammy bar the results may vary.