The way I memorize the dhamma is I have a mental map of the 8aam (noble eightfold path) in my mind.
The 4NT/4as (noble truths) is covered under compartment #1, right view.
of the 37 bp (factors in the wings to awakening), 8aam is already covered, 7sb (awakening factors) I file under samma sati, since sati-bodhi-anga is the first of the 7sb, for the 5bal & 5ind (powers and faculties), only saddha (confidence) is a new, the other 4 of the 5 are already covered in the 8aam.
saddha I file under right view, serving as an aid to provisional right view until one can discern truth directly.
4pd (padhana, exertion) is exactly the same as right effort,
4sp (satipatthana) is defined exactly the same as right mindfulness
Which leaves 4ip (iddhi pada) and saddha as the only unique factors in 37bp not covered in 8aam.
I file 4ip under right concentration, with this memory mnemonic: samadhi has 4 sets of teachings to make it right samadhi. 4pd, 4sp, 4j (jhanas), and 4ip to perfect 4th jhana to make it capable of the 3abhinna.
So that covers the 37bp.
Yoniso manasikara and appamada are both described as the boss, leader, the elephants footprint, the “cause” of the 8aam arising and being developed, so that is a direct link to 8aam that I use to cover those teachings.
what other important indispensable teaching am I missing, and how does it map into 8aam?
Maybe not as indispensable as the 37bp (otherwise they would have been included in them), but I would suggest the following Dhamma (I list only the new Dhamma not included in your lists):
the four factors for stream-entry (SN55.50), it adds:
– 1) associating with good friends,
– 2) hearing the true Dhamma and
– 3) practising in accordance with the Dhamma
things to do in order to make the breakthrough (SN56.34), it adds
– 1) zeal,
– 2) enthusiasm and
– 3) being unremitting
the seven good qualities (MN53 11-17) , it adds
– 1) faith
– 2) the two protectors of the world: shame of wrongdoing and fear of wrongdoing
– 3) learning/remembering
as part of the gradual training (AN4.198), the trio:
– 1) guarding sense doors,
– 2) moderation in eating
– 3) intent on wakefulness
Transcendental dependent-origination (SN12.23), it adds:
– 1) joy
– 2) knowledge of things as they really are
Do you know if there is a sutta name for the 37 factors of awakening? For now I only found ‘the things that I have taught you’. I am trying to find a term from the sutta that summarize them as 7 sets of Dhamma. I think the use of 37 is misleading because it assumes that they are 37 different Dhamma, which is not the case at all, they are overlapping in many places as you summarized very well.
I’m also trying to reduce the teachings to a simple map that include as many Dhamma as possible, in order to guide my studies and to categorize notes etc; for now I’m using this 1st-order structure:
Diligence & careful intention (as chiefs of the kusala dhamma)
4 factors for stream-entry
In order to make the breakthrough (7 dhamma)
Gradual training (composite version)
Things that I have taught you (the 37bp, incl. the 8aam, etc)
bodhi-pakkhiya (awakening-wings, or awakening-aids) is a non EBT term used in commentaries. I believe it refers to it as seven sets of bp. In the EBT, those 7 sets, consisting of 37 factors, is never given a name, much like other groups in the EBT. I’ve adopted 37bp because 37 really stands out, and as an oral tradition memory mnemonic, it is perfect for that.
There was a professional team sports player who legally changed his name to “metta (first name) world peace”, and his jersey number was 37. I know he had a therapist he used for years, and based on his jersey number it’s pretty safe to guess his therapist was theravadin.
Also in AN 3.16. This is a particularly important sutta, because the buddha gives specific instructions on wakefulness with specific sleep times, and the proper way to eat. guarding the sense doors falls under right effort as is covered, but those very specific eating and sleeping instructions are important on the path, and aren’t explicitly mapped into 4NT, 8aam.
SN 12.23 to me is just a slight derivative of 12ps (dependent origination) combined with 7sb (bojjhanga), with a couple of more factors to bridge between 12ps->7sb->nirvana, so it doesn’t really add any new information not already in 37bp.
Of course I’m just talking about my mental map and my preferences, everyone else working on memorizing has to use whatever makes sense to them and is most inspriing.
Yes, actually after posting I realized I was slightly off topic because the lists I made are more for study and written notes, while I believe you were talking about a model which comprises as much dhamma as possible while being short enough in order to be recorded in memory and used as a tool in everyday life and medittaion. The eighfold path seems indeed a good choice: enough items to cover most kusala dhamma and short enough to be quickly recalled from memory and used at any time and in any situation.
Thanks, I did not know that bodhi-pakkhiya were reffering to the 7 sets and not to the 37 factors. In that case I’d be quite happy to use it since there is no generic terms in the suttas. And it is a nice poetic name moreover.
Do you know where bodhi-pakkhiya is mentionned in the commentaries? I’ll try to find a reference for future use.
IN DN 27.16 it looks like it’s referring to 7 sets of dhamma that lead to nirvana.
There are a few more references in SN 48, where bodhi pakkhiya looks like it’s talking about 5 indriya.
AN 5.56, not clear what bp is:
“Therefore, bhikkhu, you should train yourself thus: (1) ‘I will be guarded in the doors of the sense faculties, (2) moderate in eating, (3) and intent on wakefulness; (4) I will have insight into wholesome qualities (5) and will dwell intent on the endeavor to develop the aids to enlightenment in the earlier and later phases of the night.’ It is in such a way, bhikkhu, that you should train yourself.”
in AN 6.17, not clear what bp is referring to:
“Good, bhikkhus. I too have never seen or  heard of such a thing.
94“Therefore, bhikkhus, you should train yourselves thus: ‘We will guard the doors of the sense faculties, be moderate in eating, and be intent on wakefulness; we will have insight into wholesome qualities, and will dwell intent on the endeavor to develop the aids to enlightenment in the earlier and later phases of the night.’1282"" Thus, bhikkhus, should you train yourselves.”
in AN 9.1, sam-bodhi-pakkhiya is referring to 9 types of meditative or prerequisite practices different than 37bp
In SN 48, indriya samyutta, it appears about 5 times, each time seems to be referring to 5 indriya, such as:
“Bhikkhus, just as among animals the lion, the king of beasts, is declared to be their chief, that is, with respect to strength, speed, and courage, so too, among the states conducive to enlightenment235 “” the faculty of wisdom is declared to be their chief, that is, for the attainment of enlightenment.
3“And what, bhikkhus, are the states conducive to enlightenment? The faculty of faith, bhikkhus, is a state conducive to enlightenment; it leads to enlightenment. The faculty of energy is a state conducive to enlightenment; it leads to enlightenment. The faculty of mindfulness is a state conducive to enlightenment; it leads to enlightenment. The faculty of concentration is a state conducive to enlightenment; it leads to enlightenment. The faculty of wisdom is a state conducive to enlightenment; it leads to enlightenment. 
as for how bodhipakk is used in commentary and subcommentary, in DPR search you have to check those options to include in the. doing a quick glance through, that search produces a lot of hits, but my pali isn’t fluent enough to get a sense of what its saying.