I guess I'm not really sure what the distinction between mindfulness and concentration is!
Mindfulnes (attention to) becomes concentration. As you've noted, part of the head pressure comes from wanting (to do concentration)/ missing (the pleasantness of concentration), wanting/wanting to not want. The mind is going off its object (breath) and getting into a "hungry" emotion. One really must go to the object with utmost care, while staying relaxed and light hearted.
If the mind minds its object willingly, receptively, it will enter concentration.
So initially, when one sustains the mind on the breath for a while -- say 20-30 minutes (but this can happen right away for others, too) the mind will then seem to brighten. (Before this can be a little light show and be part of coming-going discomfort or figetyness.)
When the mind gets well versed in this brightness, it will start to experience an almost athletic energetic joy.
Now we're talking about an initial jhana: piti. Joy.
These are practices that can seem a little far-fetched, but like any training there are reasons for this initial jhana training.
So one starts with just minding the object (say, breath) with real care, just the way one would pay attention in a friendly, close, relaxed way to something one finds beautiful/entirely lovable in a non-grasping way.
Honestly, no one has the ability to know you like you can know yourself. Some people have "previous supporting conditions" so they are actually well beyond the first jhana...and are naturally more likely to drop into a fourth jhana mind: tremendous, engaged/receptive equanimity, and this capacity exhibits in daily life as well. This relates to the Analyo quote in Ian's post: sati (smriti, Sanskrit: memory): is what causes the mind to start to choose beneficial actions increasingly over troublesome actions.
So part of me really appreciates the zen trainings (to which community you've mentioned some attraction) that don't place people in jhanic/insight frames, but start a practitioner which just "mind your mind". Just sitting (zen, shikantaza) however can be such a shapeless training field that people often feel lost or unable to use it to bring practical relief in life. So here in this thread we are all getting into a therevadan frame work, but there are many ways to approach what is already going usefully for you in this early practice: ability to sit and know that mind is still, unprovoked, coming off of emotional turmoil.
To me what you've already mentioned is very useful base and I question directing such a mind towards a Therevadan concentration framework to the exclusion of others (and one you've mentioned). Concentration is mindfulness, it is just mindfulness -- real care and steady attention to an object -- while learning not to peel off at every other thought, staying relaxed and friendly with the training, friendly with the mind when it uproots for something and friendly with the body when it's had quite enough.
Several of us are big fans of Analyo's book (see Ian's post): it is immensely practical and dense and well-documented (there is one wrong footnote that I know of). If you pick it up I'd give yourself permission to start anywhere in the book you want. It provides tremendous structure, but never feels far from any school of buddhist mental trainings, in my opinion.
**You are already showing signs of knowing exactly what to do (what not to do); then it's repeat with patience/openness/no expectation and replacing that with just closely paying attention as if to an sleeping infant or as if to something you really are keen to attend to, and being relaxed in the body.