I did a repair of Word and also tried the trick for a corrupt document, neither had an effect. I then had another look at my advanced copy/paste setttings and set them all to default.

This seems to fix it - i.e. using "merge styles" (in the pasting-pop up) or "use destination styles" (in adv. settings) when pasting within the document will erase the footnote reference style from the footnote marker. This seems... not how it's meant to be, to put it mildly. Would be curious to know whether this is in fact normal word behaviour that other can replicate...?

But at least I think I can cut and paste now without needing to double check my footnotes every single time, so thanks!