So he did. I'd forgotten that. It's in the DT, in fact, with that note attached: Prince Heathen. Not only that, there's a midi of the tune Lloyd set his rewrite to at Mudcat Midis:

Prince Heathen

As it happens, it was I who supplied the midi. The lyric is very much in Bert's style; and barely half of it is genuine. It's a good piece of work, of course —his re-writes almost always were— but there isn't much left that's traditional in it, so, as I said, it can tell us nothing about the song's past history. I think he may have gone a bit too far in this case, perhaps: Martin's re-write sticks to the basics and avoids the temptation to introduce new material or indulge in fanciful imagery; and is the more powerful for it, I'd say.