First - Floating
I have on occasion noticed a slight floating sensation with both the D404s and Exedras. The first time I noticed it I had the bike completely checked out. In case something was loose or out of place on the back end. Everything checked out fine. Now I just ignore the sensation and power on through. At this point I no longer feel it so I think it was just a floating feeling not a real sliding. Perhaps the suspension compressing or something.
Second - Tires
I know the name Bridgestone creates visions on cupping and noisy rides but. The new Bridgestone Exedra Max tires are worth looking at. It's the Max not the regular Exedra. They are far superior to the older tires, have multiple rubber compounds, deep treads and come in the right sizes. I put a set on mine at the last tire change and I have been very happy with them so far.
Mike