Irishman: There really are two questions that we are interested in, and this early quote in principle could be relevant to either. First, is this, in fact, the modern phrase? And the answer appears to be no, the lecturer was just referring to the length of a bandage. If bandages of this type instead came 20 feet to a roll, he would have said “use the full 20 feet.”
The second question is whether nine-yard bandages might be the origin of “the full/whole nine yards.” And the answer is, well, maybe, but we don’t really have any evidence of that. This one obscure example aside, hardly anyone was referring to nine yards of bandages. And there are lots of things that come in measurements of nine yards and are candidates for the phrase’s origin. Nine yards of bandage is not inherently more plausible than, say, nine yards of cloth or a document nine yards long.