I too was at the same weekend with Andy Cutting last year as Julian and remember his Memory Palace ( map ) comment.
He also said given a new tune, he will play it for at least a day, looking at all the ins and outs of it before embarking on a particular way of playing. From previous threads, I think Andy will take a full day and regard that as a working day, so not a couple times through the tune a few times during the day but a proper 'working day's' worth.
Playing a tune continuously for a day must get it into the brain so much that you can automatically play the tune whilst improvising an accompaniment or working out which way to go.
You can improvise on the fly if you don't need to think about what notes come next.
I's like anything. Once you know what you are doing and where to go in a particular morris dance, you can put that down to automatic memory, you have freed up the brain so you *can* think about how to improve your performance in a dance, better timing, little nuances that make the dance even better.
That's my take on it.
Q