Glad to hear you're not experiencing the going-to or staying asleep issues! As far as REM and deep sleep and the like, I found the various delta wave purveyors talked about, of course, sleep hygiene as they call it, sleep cycles, REM, Non-REM, and deep (restorative) sleep. Without going into the side issue here of whether one can stimulate lucid dreaming and that type of thing, which I was also interested in at the time of investigating the delta waves, I was interested in daytime creativity being aided by other brain waves recordings as well. The delta wave people had alpha, theta, etc. recordings as well. At any rate listening to waves tones can be helpful in brain entraining I think it's called.
On the topic of REM sleep, I have taken up the 'earthing concept via grounded mat' as of last night, for the first time, and I must say there was a significant amount of REM over what I've been managing to experience for quite awhile, going through thyroid makeover in these last 2+ years.
In one vivid dream, my sleeping subconscious mind combined the sensations of IBT (not quite sliding off the end of the bed anymore in actuality since my husband lessened the initial tilt a bit versus what we started with, after we undertook it again recently) with a sense of being draped backward over a round real-size Earth -- I am not very visual typically in dreams but anyhow it was kind of like that. (I had read in the earthing literature that came with the mat about it taking the Earth itself as the source and getting negative ions by utilizing the electric potential of all the lightning strikes every minute planet-wide.)
See the book "Earthing the most important health discovery ever" (I say from my personal experience so far that IBT is greater and as universally available and as basically low-to-no-cost to try out, but all this works together in harmony wonderfully I say). Page 255-7 in the paperback version, in Appendix A 'The Physics of Earthing -- Simplified' talks about Earth's surface electric potential and its being renewed by the lightning strikes.
One other thing, there may be a lot behind one's personal readings of this and that (e.g. BP, pulse, etc.) which may have to be considered in a whole picture of what may be going on in one's life/health.
For example, my pulse was always around 90-100 lifelong despite much aerobic effort to train it downwards (jogging 7 miles per day at 8 minute miles for a long time gave me a lot of good weight control and breathing training and I was considered a fitness specimen by all the doctors I was trying to get help from for my hypothyroid issues so they just suggested I go away and not bother them since I was obviously fine, and if I wanted something as an Rx they could give out some antidepressants and similar plus had excellent samples of the latest and greatest such stuff.
Despite all this so-called perfect health and lab tests for all kinds of things (at my own expense) which showed 'all was well,' I felt horrible.
Blood pressure was 140/90 at the best and I had the 'white-coat syndrome' when I saw them coming as well (to take measurements).
But when T4 generic levothyroxine failed me, thyroid tests readings went sky-high, and I was beset with incredible fatigue and all kinds of horrible hypo symptoms eventually, starting February 2016, I was horrified to find my BP going up all of a sudden to readings like 173/110 after merely slowly climbing 17 steps up to my apt from the first floor (I could no longer even walk a mile let along jog) and I went into a sheer panic about it all. (Apparently, it was all that cortisol spiking or whatever but little did I know at that time.)
Starting with some spray-on magnesium (to try to calm down) and pursuing various hypothyroidism-treating dietary modifications and other things, I have gotten the pulse down to 85 by day (random readings here and there once in awhile just for grins anymore, since I can tell what it is pretty much anyway) and in the 60s lying down in a meditative calm state.
I use my oximeter to gauge BP since it does oxygen levels and pulse, since seeing a BP monitor still gives me a jump in BP, admittedly psychosomatically. The last time I used my BP monitor to actually take it, it was 130/70 I think, and I was anxious just hearing the thing crank up with its little 'motor' noise.
Don't push the IBT concept I say, it may be your subconscious mind is not on board with the idea.
But good luck and good fortune in your health endeavors and discoveries, all the best and let us know / hear about, how it's going!