There is just one other skill in my mind that I fear I may be playing a role and that is the use of good textbook fingering. By that I mean a good formula to know when which finger to put on each note. 90% of the sheet music online seems to have no fingering. And I do not wish to pick up any bad habits that may affect my long-term piano technique.
I think, at the same time, you should not be afraid to think of fingerings on your own and try to see why they do or don't work. I've acquired a decent grasp of fingering over the years, to the point where I don't have to think about it consciously while improvising. I think one of the factors which played a major role was improvising, and discovering fingering logic on my own. Only trying to copy fingerings from other publishers will not give you any confidence in your internal logic behind fingering, and it will be hard to make the transition to fingering spontaneously.
To counter this I've been doing a long process of slowing down videos and writing down which finger, 1-5, experienced players press each note in famous scores. Do you have any opinions on how to learn correct fingering during the process of learning how to hunt and peck at the notes?
I would suggest imitating how they are moving their hands, rather than writing down the fingering. Otherwise, for example, if they transition from 5 to 1, they might do a complete lift of the hand, and you might strain your hand trying to do an awkward stretch. Imitation won't be perfect, but it will be much better than simply reading which finger to press where. At any rate, there are multiple ways to finger a passage -- at the beginning, I think it's more important to achieve comfortable and secure hand movements. Another tip is to watch the hand groupings rather than the individual notes. See them in connected groups of 4-10 notes and how they interrelate.
I'll not look at hands unless it is required for me to learn notation or a leap
Not at all, you should definitely look at your hands, or else you will develop poor technique. You're possibly overthinking the fingering aspect, while at the same time you don't realize how important a smooth and controlled touch is at the piano. You don't just "peck" a key, there is a lot of technique involved which you need to learn, for which you certainly have to look.
timothy42b, lelle, ranjit - Gieseking-Liemer. I'll have a look into this as some night reading.
I wouldn't advise reading that book. I mean, you can read it for fun, but it is meant for advanced students, teachers or pianists, not for beginners. As a beginner, it's very easy to misunderstand the things he's trying to say -- and it's not clear whether many of those mental techniques are even practical for seasoned pianists.
For a free book, to be honest, I'd suggest taking a look at Fundamentals of Piano Practice by C Chang (the pdf is available online). Not everything he says is 100% correct, but it was one of the first books that I read, and I found his ideas to be very useful to start thinking in the right direction. But, as with everything when self-teaching, discernment is key. You need to do a lot of mental weightlifting to self-teach effectively, figuring out which things work among a sea of conflicting information, constantly questioning whether you understood something correctly, even if it seems obvious. Read the posts by bernhard and others on this forum as well. There are hundreds of posts, but if you're a fast reader, you'll get through them soon enough.