I made a mistake; the PhD paper is on a completely different subject. Nick Nourse wrote about the one-stringed fiddle for The Galpin Society Journal in March 2020. I've checked my email exchanges with him and in answer to my request to read it, he said that he can't provide me with a copy, as it is subject to a 5 year rolling block on public access. I have friends in the academic community, who may be able to get it.
Here is a link to his University of Bristol profile:
More from Mike Bostock's research into early English banjo, has revealed another reference to the one-string fiddle, this one from the mid 1870s, as played by a member of banjoist Harry Hunter's troupe.