Hi Debbie! I just pat the damp quilts on the floor and it dries pretty much where I leave it. However, I do have a confession to make!
This is the same floor that I use to spread out beach towels and starch my fabrics before I cut out my pattern, and there is always a slight residue of dried starch on the floor.
Because of that starch, my quilts pretty much stay in place, and I actually have to peel them off the floor when they are dry!
Of course, I've never had to make a quilt block up to a specific size because I make quilts to use, not to hang where the dimensions would be scrutinized. I do know that after they are dried like this they hang beautifully in shows!
If I were protecting a wood floor with a layer of plastic, and really wanted the quilt to be a specific size after it was dry, I would probably tape the plastic securely to the floor (painter's tape?) and mist a fine spray of starch over the plastic before I pat it into shape. I've never actually had to do this, but I don't see why it wouldn't work.
If you try it, please let us know how it works!