Greedy kite, I think you've hit on yet another viable solution since the preamble does not necessarily preclude rearranging the letters elsewhere rather than replacing the perimeter letters. However, why drape the quote around the grid? The "thematically appropriate position" according to the original text is on top of the grid. That phrase has been puzzling me for some time because trailing around the perimeter is definitely not "thematically appropriate."
It's yet another aspect of the puzzle that has not been thought through, it seems to me.
Of course, normally if a Listener puzzle requires writing outside the grid, that is clearly signalled, but a newcomer to the Listener is not to know that, so could well choose to be faithful to the thematic text and write the quotation above the grid.