Just to muddy the waters - don't forget the other meaning- pertaining to tar !
However I seem to remember another song which mentions tarry woo. No Ihaven't missed a letter. I cannot rember whether that refered to the natural lanolin in wool of whether it was wool with a lot of tares or burrs in, which had to be got out before the wool could be processed.
"We tarried and shifted til we were quite fast."
We lingered and managed until we were very hungry