Just bit the bullet and spoke to Apple support. They said I need to download El Capitan from the App Store and install that & that I should then be able to restore from Time Machine. Apparently High Sierra isn’t compatible with my MBP, but it would be nice if it had just popped up a message saying that, rather than wading in and trashing it.
She said Sierra isn’t currently available and she doesn’t know if it will be again, so it looks as if I’ll be staying on El Capitan. Yay. Isn’t it great when things just work?