To kind of piggyback on here since you described your experience very well, I'll give my own as a contrast to yours:

Mine seems similar. Instead of piloting a body I just am my body, and I don't perceive any screen. Instead of an "area between me and the screen" I just have a completely separate workspace of sorts where I can visualize things. But - and this is where I differ from you the most I think - in my mind that workspace is quite separate from my field of real vision. If I concentrate I can kind of overlay them, but it feels very artificial.