I think what we do at night when we're sleeping ---the dreams and nightmares are an example of thinking without words. It's not musing, it's our brains sorting out the days events, our fears and problems ---and it's almost all language-less ---our dreams and nightmares are symbolic but they are our way of making sense of everything. The deepest form of thinking we can do because it's our subconscious working.
You have well explained what people mean when they say they "think without words." Those who do it in the daytime are those who have never quite figured out the difference between the dream state and the awake state. This goes a long way toward explaining the bizarre and absurd things such people believe.
...dreams and nightmares are symbolic but they are our way of making sense of everything ...
This is no doubt true of the psychotic whose consciousness consists of unexplained and causeless feelings and desires, mystical experiences, and the constant sense of terror that the world is a mysterious and unpredictable nightmare and he is inadequate to deal with it.
For the rational, study and reason are used to comprehend the nature of the world and their own nature. This comprehension is called knowledge. The product of this process is a non-contradictory hierarchy by which rational people "make sense of everything."
It is very sad that in this age people can believe their deepest form of thinking is dreams and nightmares. You did choose the right word, "deep," however. The highest kind of thinking, is that clear, lucid, and cognitive reason that ruthlessly demands truth which can only be understood by means of explicit concepts which are comprehended by means of words, that is, language.
To promote a non-linguistic form of consciousness is to promote a kind of insanity. A non-linguistic consciousness is appropriate to the irrational animals, in human beings, it is sickness.
Hank