Thanks for digging, Smiffy. A 48 hour hire would give me time to try a few stream downloaders on the address. There may be some other Jimware that recognises a stream coming in and saves it as a file too.
In the past I've 'discovered' mp4s in the page source for direct download. Neither of those sites look technically sophisticated, so you might get lucky.
Just my completist thang. I think it's a beautiful bit of prose - all the better for being spoken. Burton's telling of it is very good; and, for its curiosity's sake, my Christmas card this year. But the best reading of it - better than even Thomas's own - is this one, by Bob Kingdom for Beeb 2: https://vimeo.com/274684677
One of the early album pressings of Dylan's reading included three loose leaf engravings by Fritz Eichenberg, which are now worth a bit. I don't know if was that one, though.