I think Zen tries to capture the commonality of the joints between the myriad elaborations of Buddha's insight, including the 8-fold path. The common element is how the activity of being aware/responsive to what's presented puts one in right relationship.
At each point philosophically or otherwise, the prescription changes to reflect what's presented, but the basic relationship (meditation) doesn't. Thus, though Zen is ostensibly just a practice leg of right-mindfulness, meditation is everywhere as Buddhism is elaborated, as it must to reach out to those not meditating, i.e., any moment when we are not aware, words and rules may help (barring attachment)).
What does it mean for Zen/Buddha to be elaborated in different contexts? Implicit in the eightfold path is a model of thought/action:
view (passive mental), thinking (active mental), mindfulness (passive activity of mental), speech (mental action), action (individual acts),
diligence (will), concentration (understanding/awareness),
livelihood (continuous acts)
Each of these psycho/philo-sophically precedes and is included in the other, e.g., action and livelihood establish external characteristics of actions, at different levels of analysis (livelihood recognizing the unity of an action we identify with, do continuously, and are bound to for our survival); diligence and concentration establish the internal conditions for creating such actions: make it happen/well. Thus, right action preceding the conditions (will, understanding) of action recognizes the teleological nature of actions: they are determined by their implicit objectives, and then the will/understanding performs them well or poorly. Similarly, good will is required for understanding, and good understanding is required to have right livelihood.
Understanding this precedence is important for understanding ourselves and the impacts of our actions on others. E.g., it often does no good to argue at the level of thinking; better to discover and evaluate underlying views, which are subject less to argument than to the overall feeling of "would you want to live in the world created by these views?" In a sense, to be aware of the action of one's views (certainty, habit) is to practice this question continually. Thus, TNH's "thinking" actually uncovers "view" issues. This backtracking is true of all Zen/buddhist moves. Conversely, the transformation fiat/will/understanding/right livelihood is the gambit of Zen, projected on the issue of how action becomes livelihood. Life is always emerging in this manner; for us in particular, we become who we are by our objectives calling forth aspects of will and understanding, repeatedly to form habits if not survival strategies that are more or less harmonized with others. This is as true of a child crying for food as for a Zen master meditating (spanning relations dependence -> independence -> interdependence). (Heraclitus: character is fate)
But to departicularize philosophy (= to remove the limits of our selves), Zen removes the content of the objective insofar as it can be held as a conscious object (i.e., insofar as it is a product of mind, reversing the actual relationship, as we are wont to do with the idea of creating ourselves according to notions of good and evil (original sin)).
So: does this move of Zen cause us to lose our soul?
The greek notion of soul - anima - is really more of a question, a placeholder for whatever it is that animates us, what sets us in motion. Aristotle distinguished different kinds of movement/animation, noting their inverse as types of causation: simple movement (being moved/newtonian), self-movement and replication (life), telos movement (being shaped by objectives/ends/identity, - love), and understanding movement (holding to an idea - commitment, understanding).
So our "soul" is different only in kind or style from the movement of animals or even rocks. anima animating is thus like inter-being. But our souls enable us not only to be moved, move ourselves, and replicate; but also to think and understand. He establishes a hierarchy of being (where, like the 8-fold path, each includes the prior) according to its completeness. To be moved lacks both initiative and self-definition. To move lacks self-definition, since it is moving somewhere else (i.e., the activity of moving is itself wasted, since the only purpose is to be somewhere else). To replicate is a form of not moving somewhere else, since some copy of us returns, though not us. The most perfect form of being, lacking neither self-motion nor self-definition, is nous, thought- thinking-itself - i.e., where one simply abides with the thought (e.g., mathmatics) and it moves. Seeing is similar in that in the activity of seeing, the object seen is held by the eyes, as it were. But seeing is limited to form and color and sight, thinking is not.
Zen meditation goes one step further than thought-thinking-itself (nous noein) - to nothought nothinking (i.e., not limited to the thinkable or the thinking). If in fact it is practiced, then it escapes the particularity of the thought just as thinking escapes the particularity of seeing. Note in each case one impliedly also loses one's own particularity - we see the same things (disease aside), think the same thoughts. It is further emergence, not a denial of soul. (At this stage is typically asked, how could you lose your soul?) It is further because each stage essentially perfects the prior by bringing it into activity; just as one's views are perfected by being activated in thinking, so is thinking perfected in action, etc. In each case the relationship is understood in Zen as being-aware, or realizing, or self-clarification.
(Plato models the similarity of these relations by saying that the different levels of thinking - perception, opinion, thinking, and minding - are simply analytical divisions of the same activity of awareness/perception, a line cut twice (lined) in the same ratio. Based on the geometric model which requires an orthogonal relationship to generate two identical divisions, Plato posits a Good (what you might call Right). But it's clear that we do this constant analysis without positing a God, so Zen probably only insists on this constant awareness, without inquiring into what makes it possible (according to our models).)
So the short answer is that doing meditation should make you more alive. (That's both predictive and prescriptive: if it makes you depressed then it's not meditation (that's different from encountering depression through meditation); also, it will make you more alive!)
The problem, perhaps, is that Zen teachings can be used in a self-abusive manner - training one to ignore needs (e.g., pain, hunger) that in fact exist in one. This is like trying to escape from dependency relations, where one learns the trust underlying all engagement. I would think this to be particularly true of American Zen, where students, even serious ones, do not enter the kind of dependency relationship with their teacher or sangha that Buddhists in other countries do, and where there is a social and psychological history of abuse and neglect. Our relationship with understanding is as a tool to obtain power, so we seek the wisdom of Manjusri rather than the compassion of Quan Jin. We have to be aware of inversions in the emergence relationship, e.g., where we give up hope, establish limited views, etc. This may be particularly true of those who meditate alone.
So I guess I think of nirvana only as no-suffering, not no-activity, and impermance as the law of emergence/change, and no-self as the self- understanding that leaves only the soul as activity.
Zen masters seem to mix a couple strong styles: rigid no-saying with playful everything-everywhere-even-here (SHOUT!), depending on how to rid the block to emergence from limited ideas/objectives. Rigid responds to those who go too far (willful); loose responds to those who don't go (lack of will). Love is a good practice because one acts out of love and understanding for another, keeping one active but not willful, but it's hard to avoid attachment in almost any real love relationship. Thus, in the matrix defined by the naturalness of love and the no-attachment styles of Zen masters lies our ambrosia.