After setting up another store with other content, I see that it’s the tall product images that are the root of the problem. And also that some changes I’ve made to some stylesheets somewhere have caused the padding to go bad (I realise that it’s there to create height for the container holding the image).
I guess the only fix to get around the images that are about 3 times the height of a desktop viewport is to use images that aren’t so narrow.