But I could play either Jerry Lee Lewis style, arms length from the keyboard with my head back, or Glenn Gould style, hunched over the keyboard and my head moves a metre between the two. So that's around the 3ms threshold where I (and the sound engineer above) claim to be able to detect delays, and yet I don't think I'd notice a delay between those two playing positions

Your brain is very good at compensating for noise and delay in a feedback loop it controls so it's hard to say one way or another. Maybe it feels like a difference in expression instead of a change in delay? A better experiment would be to, like, hm...

let's say you're standing a few meters from a metronome and a musician playing to it. If the musician is close to the metronome, you will hear their playing on beat. The further the musician plays from the metronome, the more delay between you hearing the metronome and their playing, unless the musician stands between you and the metronome. When would you notice the delay?

Yes, something like that. As I mentioned elsewhere, I wonder if the result might be affected by the acoustics of the room as well as the physical proximity of the sound sources