Wow, that is great control you have there Embrace. Congratulations are in order!

When I find myself in a False Awakening, that alone is enough to knock me back to the physical again. I have learned how to control my Lucid Dreams, but still get the "knock" out of the Astral blow from my False Awakenings.
Yeah, most people don't realize they're projecting.
Being able to figure out you're actually projecting when you're having a false awakening is quite the accomplishment.
I think I've only ever figured out a false awakening once. LoL
I don't think it's actually that unusual to be able to maintain awareness during a false awakening and use it for projection. For me, that is almost the only way I've ever experienced AP. In fact I had one such experience this morning, albeit a very short and pretty freaky one:
I had just had a long vivid dream and thought I'd write it down in my journal while still in bed. As soon as I started writing I sensed something was wrong - the pen didn't write the way it should. I immediately realised I was having a false awakening. In order to "stabilise" the experience I just kept on writing for a while and then I thought, well why don't I get out of my body. I also checked the time, and the time was obviously wrong, so that confirmed I was having a non-physical experience. So I just got up, out of my body, very quickly and smoothly. At this point, for some funny reason I thought, "Well I'm out of my body, so now I should open my eyes to see better". As soon as I did, I felt somebody's presence right next to me. Like somebody was standing right there, almost up against me. My first thought was that it was just myself or something, but I quickly realised it wasn't "me" or my body. I freaked out and woke up with a gasp of fear only to find out that this "someone" was my girlfriend lying there at my side in bed. She was at least as freaked out as I was

The reason I saw my girlfriend next to me was that I had opened my physical eyes while out of body and was getting visual input from two sources simultaneously, which is a typical problem for me. But at least I have finally figured out the solution - I need to stop thinking about opening my eyes, this is some bodily habit, actually I think I can see perfectly well in the astral without "opening my eyes".
And just for reference - this experience may have been induced by the SILD technique described in a sticky under Astral Consciousness - I had done the exercise about an hour earlier.
As for projecting from false awakenings, then these have happened when I've tried going to the bathroom, but realised I'm dreaming because suddenly there was no toilet in the bathroom or tried looking at my watch but realised the time was unreal and in similar situations. In fact, I haven't had many experiences where some sort of a false awakening hasn't been involved, but of course, it will depend on the person.