Hi guys,
I'm no expert on sleep, but have been a shift worker for about 10 years and can say from experience that taking yourself out of REM is very hard on the body and disrupts the circadian rhythm. REM is your most important time of sleep for body recovery.
Having said that, I believe that continuing with your meditation practice will bring you down into the same waves that are in REM eventually. I'm just piecing things together as I write, but what you're describing might occur later in the more advanced stages of meditation. Maybe these dreams are the reality, your ego/identified self stripped away completely, leaving just your being as a connected part to the universe.
I am a beginner as well and haven't experienced what either of you have, but then again, maybe that's the point too. At any rate, please post if you do give it a shot and what your experience was.