Steve Kind wrote:
[...]
If I do raise the whole patio it will involve a 3-inch layer of sand
accross the whole area - I'm a bit disturbed by the suggestion that this
might in itself damage the tree

The roots in question are in sand (?) under flagstones already, so no
big risk there.

How about lifting the flagstones that are raised, trimming them to
better accomodate the roots, and putting them back down again? Done
that way, you can do one flagstone at a time.

Care to share photos of this project?

Una