Thankfully, we do not need to reinvent any wheels here. We just need to organize what's already been found through over a thousand years of Martial Arts exploration and assign some language to it. So let me focus on trying to do that.
First, it is important to note that these States can be thought of as mindsets in Martial Arts terms, and that they correspond to 1st Quadrant (Personal) selves. Wilber's concept also holds true: every self has a body. So waking corresponds to gross physical stuff. Dreaming corresponds to the subtle body. Dreamless sleep and witnessing correspond to the causal self, and finally the non-dual corresponds with Oneness. I put forth that all of these items are discussed in a Martial Arts context in detail already by many sources and here's an attempt to lay it out:
Starting from the top, No-mind seems to be a correlation to dreamless sleep and/or witnessing. In particular, No-mind requires focus on no particular thing, especially not focus on focusing! It is the ultimate letting go, and it is non-directional. During the State of No-mind, things arise as they need to. From a Martial Arts perspective, this is basically the arising of victory. Musashi and Takuan speak of winning battles through No-mind, where there is no separation between you and your opponent. Here's a great quote from Sun Tzu about that:
If you know the enemy and know yourself, you need not fear the result of a hundred battles. If you know yourself but not the enemy, for every victory gained you will also suffer a defeat. If you know neither the enemy nor yourself, you will succumb in every battle.
The way I read this, if you are in No-mind, i.e. causal consciousness, there is no separation between you and other things. You are "Not Two". So, really the idea of any conflict at all is silly, or at best beautiful because it is a perfect expression of something rising out of itself, as itself. What is a winner in that case? There is only One, so it's not really relevant in this State who (or what) wins or loses. On the other hand, the farther you are away from No-mind, the better your chances of losing will be, especially since losing actually exists on that level of separation.
Mind of Water
This is a term used a lot by the Martial Arts practitioners that taught me, and their teachers, and so on. I did not see it used anywhere else until I read Takuan, Musashi, and Sun Tzu. At this point, I'm suggesting (but still exploring the possibility) that Mind of Water corresponds to subtle consciousness, i.e. dreaming. The ancients describe this state as never letting the mind stop at something, because whatever the mind stops at will cause it to be cut down. (I'm paraphrasing Takuan here.) Meaning that the mind should flow around and not focus attention on any particular thing, but when it needs to then it can. At rest in the Mind of Water State, the mind is like water flowing past a riverbank. Thoughts come and then flow onward down the river without stopping by for a visit. Then the next thoughts come down the waterway and move onward just like the last. This feels like a basic relaxed mindset and being at ease but alert.
Satori: Mind of Mirror and Mind of Moon
The best example of Satori comes from a book I read by Dan Millman where his teacher held up a knife and told him he was going to throw the knife at Dan's face and Dan had to catch it. The teacher wasn't serious, thankfully, but was merely proving a point and showing Dan what Satori felt like. Satori is total pinpoint concentration devoted to a single thing. In my training this has been called Mind of Mirror. When you punch through a board or a ribcage, your focus is ultimately devoted to a single point just before the impact. It zooms in at the last split second.
Mind of Moon is the opposite: open awareness. The ancients touch upon this concept when they discuss where the eyes go during a confrontation. Many argue for having the eyes focused on no particular thing, but instead seeing everything all at once and zooming in with Mind of Mirror when the final action is called for in a strike. The eyes will train the mind to go where it needs to, and how to switch between Mind of Moon and Mind of Mirror accordingly. Daniel Goleman in his new book, Focus, alludes to "top down" and "bottom up" attention. Top down attention is basically Mind of Mirror. It is conscious focus and thought directed at a single problem or object. Bottom Up attention is open awareness which allows the unconscious brain to make connections between things it sees but may not have put together consciously.
Both of these States, I think are gross States, because they deal with physical attention, but at the same time they can be portals to other States. For example, Mind of Moon and Mind of Mirror are both the first steps to two different kinds of meditation. Hold one of those States long enough, and you will begin to rise up through Mind of Water and eventually to No-Mind. So I think one thing that Martial Arts points out is the fluidity of States and how they can (and do) flow into one another. It seems to me that you don't just achieve a State and stay there for any length of time, just as you don't stay awake for 24 hours per day routinely.
As always, this is a work in progress so other thoughts or speculation on how States might be dealt with in a Martial Arts context are welcome.
The other thing that makes this a giant mess is how States are perceived differently at different Stages. This post is just a basis, colored by whatever my own Stage is. In future posts, I plan to sort out how other Stages might interpret these same States.