1. Technique follows from force of will: This might sound strange, but try and imagine yourself playing a difficult technique, at tempo, to the point where you can, as far as possible, see in your mind's eye the sound being produced. Observing performances by professional pianists can help with achieving this. Once you have this clarity, attempt to execute the technique, at tempo (don't practice slow as it will distort the aural image). It feels like "willing a sound into existence", and I've found it to often be very effective. This also would partly explain why some people never acquire certain techniques -- the will to produce the sound needs to be there in the first place. It is easy to give up on something thinking that it is too difficult, and hoping that other "easier" work will eventually translate automatically to mastering the difficult thing, but it doesn't seem to work that way.
2. Play it slow after you know you can play it fast: This is partly in continuation of the previous point. I've found slow practice to be much more effective when you "know" that you can basically play it at the required tempo if you have to. This frees you up to think of all of the minor details, and possibly makes it easier for you to find out which details need to be focused on in the first place, because you can imagine (or play) the piece at the desired tempo to check whether they would work.
3. When implementing changes to a piece of music, try and orient your mind in a way that the change becomes "self-evident": I've found that this is the only way to permanently effect the change. Note that "self-evident" is different from an intellectual understanding. You need to figure out an angle from where it is inevitable that the modified way is the "correct" one. For a trivial example, you might think of a certain figuration in threes instead of twos, and those threes automatically suggest a natural fingering which you subsequently apply.
4. To overcome speed barriers, try and get your mind into a state where you are concentrated and literally thinking "faster". Playing something exciting which ramps up in tempo can be a good way to get into such a state. Note that here, I'm talking about speed 'barriers', not about the polishing stage. I've mentioned this quite a few times recently, and I still believe it's true. Often, playing something faster is like learning to gallop instead of walk -- there's no way to get better at galloping by walking, you need to either keep trying to gallop, or consciously improve individual aspects of the galloping motion. Walking with a faster metronome marking won't cut it. Also, when you are extremely focused, time seems to pass more slowly. Try and use this for improving speed by going on for short bursts of time while very concentrated, and trying to subjectively feel time pass by you in slow motion.
5. Playing something faster than intended is a good way to aid memory and observe the structure of a piece: It's like fast-forwarding an audio cassette -- you end up thinking more about the bigger structures.
6. Listening to music right before you sleep is surprisingly effective: Try to get the music looping in your head. It will drive you mad, but your learning rate will increase dramatically!
... Creating music and art is what we want to be doing, not being overly concerned about technical problems we cannot solve efficiently...
Observing professional pianists is good but I don't like the idea of mimicing movements or even the sounds they produce. One needs to come to conclusions about their own two hands after a lot of training, to try and take a short cut by simply copy pasting the idea from what you see from others just doesn't leave you with a full understanding of what you are doing.
Simply trying to play something at tempo if you cannot control it will leave you with estimated playing and muscular memory which needs to be chipped away and remodelled.
Developing with easier pieces allows you understand the process of learning pieces better. This can be difficult to understand when one only has themselves to look at. To simply give up easier pieces and stubbornly work on difficult pieces is something a number of people attempt and there is a high failure rate and even higher propensity to invest excessive time... they can act as a catalyst to ones progress but it does little to sharpen ones practice method, reading skills and a larger overall understanding of musical language which should be at a high priority.
I find if I have to talk about technique in great depth with a student in a lesson then the situation is a failure. Playing the piano is really not about technique, it can seem that way but we don't need to approach it in this manner. Sure some people only want to play the piano because they want to play difficult works, if that is their passion good on them, but this is not the only journey one can and should take with piano music. Creating music and art is what we want to be doing, not being overly concerned about technical problems we cannot solve efficiently.
I grew up playing the piano, before the age of 3 I would play on it, but not in the actual sense of playing the piano to create music that occured after the age of 3. I never thought about technique at all, not one bit. This freedom of thought really effected how I learned at the piano, it was about creating pleasing music, yes I liked doing acrobatics on the keyboard but it never was in the forefront of what caught my attention at the piano. I didn't listen to recordings (which is all too easy these days and videos, I very rarely saw videos of other pianists back before the internet!) and consider I must learn this piece bcause it is very difficult and it will impress others and I must prove myself! If I heard something nice I would want to learn it but it had nothing to do with difficulty and all to do with if I liked the piece or not. My music journey always has been about creating music first and foremost. You do get a lot of people these days who approach the piano absolutely the polar opposite, it is all about techcnique and exactly what your fingers are doing and to prove that you can play these difficult pieces, prove to who, for what point, what about the music?
So let's say you take your time learning the notes then instantly push yourself to play at tempo if I am understanding you correctly here. This is of course possible with small parts but certainly not the whole piece.
It may bring interesting results for developing pianists who have little experience with difficult movements and want to experience much without bothering about complete mastery, but this certainly isn't something you want to do constantly.
In my mind speed barriers do not exist it is lack of control which limits speed. So it is about control not speed. If you can completely control a piece you can play it at any tempo even if you have never played it at those tempos before. Appropriate slow controlled practice will generate any fast tempo.
If I study something that was difficult I will go through the patterns in my head and tap the fingers while I am going to sleep. That is annoying though it doesn't help you sleep lol. It does help post practice improvement though, I tend to do it whenever I've worked on something alien.
This is fuzzy to me, I feel you need to give some examples or explain yourself in more depth.
Playing the piano is really not about technique, it can seem that way but we don't need to approach it in this manner. [...] Creating music and art is what we want to be doing, not being overly concerned about technical problems we cannot solve efficiently.
If you can completely control a piece you can play it at any tempo even if you have never played it at those tempos before. Appropriate slow controlled practice will generate any fast tempo.
Honestly I would argue the opposite, that playing the piano is entirely about technique. Without technique you cannot hope to create "art" or musical expression in general.
It's possible that this is true for some people who have naturally flexible and easy to control fingers and hands. I will say that in my personal experience this never works.
Completely controlling a piece at a slow tempo requires completely different hand movements and positions from completely controlling it at a fast tempo.
For example right now (I've been away from the piano for about four or five weeks at this point) I'm thinking about this piece and trying to play the right hand at speed on the counter.I can get my fingers to make all the correct movements up to about 80 BPM. After that it falls apart. This doesn't seem to change regardless of how much time I spend on it.
Suppose you have internalized a certain fingering for a passage, and you would like to change it. Then, you have a mental representation of how it goes. Just attempting to memorize a new fingering doesn't really work that well. Instead, I find that you kind of have to think of some sort of intuitive rationale using which the new fingering becomes evident. It's very hard to explain. It's like you remember the certain 'bounce' a new fingering has over an older one, or the specific way your pinky plays the top note of a melody, and try and internalize that sensation or 'intuitive logic' instead of the fingering itself, so that the fingering feels like it follows as a natural consequence of that fragment of 'intuitive logic'. Then, when the actual section comes up, you think of the 'intuitive logic', not the individual changes that need to be made. But the individual changes are made automatically, because they are encapsulated by that 'internal logic'. And by doing this a number of times, I find that you can effectively rewrite a previously stored memory, because you rely on the sense of 'inevitability' of the new way of playing to ensure that you don't resort to the old way.It's ridiculously hard to explain over text.
It's possible that this is true for some people who have naturally flexible and easy to control fingers and hands. I will say that in my personal experience this never works. Completely controlling a piece at a slow tempo requires completely different hand movements and positions from completely controlling it at a fast tempo (not that I've ever achieved the latter). Also I think at least for some of us, our bodies do not obey us most of the time.
I personally have a similar experience to you, and I think it is hard to generalize. My previous teacher never emphasized speed and always said that you just need to get the right, comfortable, efficient movements and speed will come automatically. When I started with her, that seemed true. My technique was very tense and aiming for speed just made it more tense. When I focused on making better motions and staying relaxed, a certain level of ease and speed did just come automatically. But then, once I was relatively free of tension, that approach stopped working. The changes in motion that I needed to make to increase efficiency were smaller than they had been at the beginning (because at the beginning my technique was awful) and therefore, harder for the teacher to describe. Now in the pandemic, without a teacher for the moment, I've found that aiming for speed, by doing short bursts on fragments of a piece, really teaches me what I need to change about my motion in detail; it just makes it physically clear to me in a way that trying to design the most efficient motion in the abstract, even with a teacher to help, did not.