The only thing from all the helpful suggestions so far, that I hadn't tried, was Regulator's one of there being hidden formatting in the template, that Word won't show. I've pasted without formatting, I've been into all the cell and table formatting possibilities that I could find (most did have the decency to be as I recalled form past exploits), but still no formatting showed itself, yet it refused to be persuaded.
However, a totally different option that I had not realised the existence of, has raised itself. Avery Design and Print software is now (probably had been for years, but I haven't had to look in the last 10 years) a free online resource. In that, I can select the template, import an image which is the text on a suitable background (the Sierra Leone flag), dump it on a representation of one cell, and voila! its there on every cell. I can then print directly. Can't actually do that today as the labels are arriving tomorrow!
So, Word and its cranky table/cell formatting can go and stuff itself, again. Thank you all, for pushing me in the direction of an entirely unexpected answer!