This is just an idea I'm throwing out there--not meant as a critique of any given methodology, at all--but there are other traditions where the aural approach is given primacy as well, and that might suit better the personality of some individual child (but maybe not yours--not trying to tell you what to do!).
Harpo's fiddle teacher plays Celtic and bluegrass music; she plays him a new tune once or twice, he reads the new tune the first time through, and then puts away the music and has it by memory from there. I "help" by singing his tunes in the car, in the garden, washing dishes, whatever (I sing all the time anyway, so it's no trouble!). I also help by turning things into duets with him (I'll either play flute, piano, or sing); I also have him play his fiddle tunes on piano by ear. He circles back to old stuff periodically, and also writes some things of his own, too. She's a great teacher--she really seems to understand his need for a certain amount of freedom, while still making sure he is making some good progress.
The piano teacher I'm eyeing for all three of them is a professional jazz pianist, who teaches chording and improvisation right away, which I think would well suit my particular kids. I do some harmony with them at home--it's a big game to them right now, which is nice--so I think their reading skills will be quite good, too.
Anyway, just a little idea...
minnie