Re: Achieving the perfect float
Actually, it's more common for the guitar to go flat after a dive-bomb or sharp after a pull-up, with the opposite direction putting it back in tune.
Sounds like you either have a loose nut (also known as a crawling nut, but usually you'll go flat after a pull-up then sharp after a dive-bomb but not always).
Check the nut bolts/screws and check the neck screws as well (I refuse to call the neck screws "bolts," they are not bolts, they are wood screws.)
Since this is a ZR trem the usual Floyd Rose physics don't apply to everything. Make sure your bearings at the bridge aren't grinding and you have the bridge balanced properly. If you're using the zero point, or whatever they call it, make sure the springs are balanced correctly according to the instructions in the manual. If you're not using it then you'll just have to make sure everything is tight and nothing is rubbing on the bridge, adding friction.