'He suggested that the remake of the Poor Cotton Weaver version of the song to the Four Loom Weaver version dates from around the 1860s during the cotton famine.'

This would have been Professor Lawrence Goldman. He proposed that an ancestral version from the 1790s, known alternatively as 'The Oldham Weaver' or 'The Poor Cotton Weaver' was followed by another version (title unspecified) around 1815, and that the song 'emerged again' in the early 1860s in response to the Cotton Famine, the mention of four looms reflecting the later mechanization of the industry.

This account doesn't really tally with the broadside evidence. The only candidate for the '1790s version' would appear to be the original 'Jone O' Grinfilt' ballad about going off to fight the French; I don't know of a song or broadside with the title 'The Oldham Weaver', while 'The Poor Cotton Weaver' - generally printed under the confusingly identical title 'Jone O' Greenfield' - is the one I'd assumed dated from ca. 1815. I know of no broadside dating from the 1860s resembling the MacColl version or mentioning a 'Four Loom Weaver', though maybe Steve can correct me if he's ever found such a thing. 'Jone / Poor Cotton Weaver' broadsides were, however, still being printed at least into the 1850s, and Harland (writing in the 1870s) tells us that this text (not the 'Four Loom Weaver' version) was 'still a favourite'.

So, I can find no evidence that there was any rewrite of the text during the 1860s, and there's nothing in the text of 'Four Loom Weaver' to connect it with the Cotton Famine. So I'm still sticking with my original theory of a MacColl rewrite. By an odd coincidence MacColl lived during the 1930s in Gee Cross, Hyde, very close to the present home of my old friend Stuart Cook, who explained the concept of the four looms for us earlier on. It's not impossible that MacColl heard the term then. (NB Stuart stated that these machines were worked by women, in contrast to the male narrator of the song).