Yes, that worked beautifully. Many thanks!

When I checked with a new document, though, I was surprised to find that not only did my revised heading styles not carry over to that (as you said it would not), but that the 1, 1.1, 1.1.1, 1.1.1.1 style didn't carry over, either. So how do I transfer that style over when I do want to? (So far, come to think of it, my method has been to make a copy of a document where I have that style and delete all the text in it.)