Yes, the "floaty" feeling is from the increased float in the pedals - your ankles and knees have much more freedom than some other pedals and does take some adjustment. It didn't take me too long to adjust when I switched, and I've never accidentally unclipped.

When you clip in your second foot, you might want to pull up on the pedal to check that you clipped in completely. I remember when I first switched that I wasn't sure if that second foot was in all the way or not because there wasn't the "clunk" that I got from the SPD pedal. There was a couple of times that I hadn't at the beginning, but that's not happened for a long time. I hope you wind up enjoying your new pedals as much as I've come to!