Stays put. No floating.
I guess that approach seals off the mashing zone from the atmosphere, but there is a slug of oxygen under that lid that adds to the oxidation load. But that is why there is an excess of meta in the wort. But using that assumption, it appears that just using a well-fitting lid on the tun serves the same purpose. I've gone to a bit more trouble with the floating cap, but I'm not sure that its truly necessary. A wort return tube and a sheet of plastic bubble wrap might be just as good.
It depends on your setup. Mine is set quite the same as Bryan's, whereas you set the lid right down on the liquid and recirculate with a flow rate that doesn't introduce an air pocket underneath.
All of these steps combined makes it so that dose rates for Meta can be reduced very low, on the order of 25 ppm with plenty of margin left pre-Boil.