This is yet another instance of a puzzle which I would have abandoned if I had not had help from this forum. Thanks to all concerned.
I found that when I had drawn the curve through the 29 letters I had to continue through two further cells to complete the closed curve. Admittedly these two cells had already been visited at the start, so that the total number of cells visited remains 29, but it seems a bit of a blemish to have two extra letters tacked on to the quotation.