I would like to know more about what you mean by "floating". I use and explain what I would call "floating" in class a lot. And I believe that Aikido technique uses a lot of this.
I would call "floating" the ability to get under your attackers center. By doing this, when your attacker tries to push on you they kind of "float" themselves up and cannot exert much horizontal force on you (because they are losing their connection with the ground).
From what I gather of your previous examples, you are maybe not talking about this. What do you mean when you use the word "float"?
I'm certainly not the definitive lexicographer here. You need to be under in order to float. Floating is more or less what it feels like if you get popped up onto your heels, you float upwards like a bubble without feeling any resistance. When floated you can be moved around easily, you can still input a push into your partner, but you basically push yourself away and it is easy for your partner to direct you where they want you to go.
Yes, you get under (it feels as though your effective center of mass is lower than your partner), but there is no physical lowering of the body, and there are a number of different ways in which one can get under, of which I have described at least two. How do you generally teach people how to get under, and when they do, do you see a difference in how various waza are applied?