I'm afraid there is a misunderstanding. My problem is not falling into non-REM sleep, usually it doesn't happen. It's forgetting. For example, I'm doing what I must, time passes, I'm still doing it, time passes, and suddenly I completely forget about it and start engaging in conversations with dream-people or go for a walk in a dream. In other words, I forget that it's a dream and what I'm supposed to do in it. I thought that it's due to not enough concentration, but I'm not sure.
J Adam G:
The best chance of arousing sufficient energy, mindfulness, and concentration is during REM sleep, which may only last for 5-20 minutes at a time.
I heard about 90 minutes per cycle, if memory serves me right. It's enough time for practice, and you can do it multiple times per night.
Spinning and rubbing doesn't really help. These things help with making dreams more vivid, but don't help with keeping lucidity.
Have you ever read The Tibetan Yogas of Dream and Sleep, or any related books? I bet you would find those really interesting!
Yes, although they aren't addressing the problem. But as far as I understand, you're supposed to do practices that are described there for more lengthy times than ~5 minutes per night in your dreams. It's too small time for any practice to have an effect. So solution must be implied.