ShyPianist: Some of the knowledge I'm talking about you could conceivably learn on your own, but could learn faster from a piano teacher.
Yes and no. What I categorically don't want is to learn one person's method of teaching. I want to appraise all the information and research there is out there (as much as possible) and form my own judgements. That's what widespread reading and personal experience can do, and attending CPD courses if that's possible, and what learning from one single teacher would most probably not do. I agree a mentor could certainly be helpful, but not simply a local piano teacher because who's to say they are any more qualified to teach me about teaching than I am myself? So I need to find a teacher who takes people up to diploma level and beyond. Those are normally affiliated to music colleges and I am hundreds of miles away from one of those. So I expect you now understand the issues. As I said there is very clearly a big culture difference between the USA and the UK in this respect.
By the way, I relate to you in this area quite a bit. And I'm telling you, it's a big world out there! I spent an entire year immersed in forums, Facebook groups, collecting materials and books, finding role models, figuring out how they taught what they taught, because I can't remember what 5 year old me learned and you find out that all these things that come so naturally and intuitively to you now have to be taught and how in the world do you do that?! It was quite an adventure finding out why in the world all these methods existed and for all intents and purposes, pedagogy does not necessarily exclude informal study! Piano pedagogy is the study of teaching piano, which is exactly what you are doing. It does take a lot of time. I was working part-time that year so I had a lot of time to devote to research.... Different students have different areas of weakness and it will be easier for you since it's just your child and you know your child's particularities. I had a sassy transfer teenager who in so many words told me the fingering I wanted her to use "hurt" instead of whatever funny thing she came up with and... ugh.. here I am like, what do you mean, it hurts?! I have never had that problem! I also realized, fingering, not an area I've spent much time thinking or learning about....
I love Irina Gorin's work particularly for teaching young beginners and I think it is exemplified well by her students' beautiful playing. She has a number of videos showing how she teaches certain skills, perhaps you'd find helpful.
Piano Safari is also an up and coming new method that I find very intriguing.